Term Structure Models with Negative Interest Rates

Size: px
Start display at page:

Download "Term Structure Models with Negative Interest Rates"

Transcription

1 Term Structure Models with Negative Interest Rates Yoichi Ueno Bank of Japan Summer Workshop on Economic Theory August 6, 2016 NOTE: Views expressed in this paper are those of author and do not necessarily reflect those of the Bank of Japan or the Institute for Monetary and Economic Studies. 1

2 Background The total amount of fixed-rate sovereign debt trading at negative yields is $10.4 trillion ($7.3 trillion long term and $3.1 trillion short term) as of May 31 (Fitch, 2016). It had been assumed that nominal interest rates could not fall below zero as long as people could hold currency. Recent episodes, however, show that negative-yielding government bonds can coexist with currency. The power of arbitrage between government bonds and currency is not so strong as to forbid bonds yields falling below zero, although it is proposed that arbitrage still works to the extent that there exists a negative limit that nominal interest rates cannot go beyond (Viñals et al. (2016), Witmer and Yang (2016)). 2

3 Background (cont.) After the introduction of the negative IOER, government bond yields not only in shorter terms but also in longer terms have fallen below zero. Furthermore, government bond yields in various terms have become more deeply negative than the IOER. Switzerland Germany Japan 1.2% 0.6% -0.2% -0.4% -0.6% -0.8% -1.0% IOER -0.75% 3M 6M 1Y 2Y 3Y 5Y 7Y 10Y 1.0% 0.8% 0.6% 0.4% 0.2% -0.2% -0.4% -0.6% -0.8% IOER -0.1% IOER -0.2% IOER -0.3% IOER -0.4% 3M 6M 1Y 2Y 3Y 5Y 7Y 10Y 0.4% 0.2% -0.2% -0.4% IOER -0.1% 3M 6M 1Y 2Y 3Y 5Y 7Y 10Y 3

4 Background (cont.) The negative interest rate policy is conducted together with other unconventional monetary policy measures such as quantitative easing and/or forward guidance. This combination of unconventional policy measures causes some difficulties in evaluating the single effect of each policy measure. Besides, negative interest rates in nominal terms had been thought to be unreal, so theories and models to deal with negative interest rates are underdeveloped. 4

5 Contribution Develop a model to evaluate the effects of unconventional monetary policy measures including the negative interest rate policy on government bond term structures. Generalize two popular models, the Gaussian affine model and the Black model. The main difference between the two popular models is how they deal with non-negativity of nominal interest rates, or the power of arbitrage between government bonds and cash. Arbitrage between bonds and cash still works in the newly proposed model (Extended model). But, it is not so powerful as to prohibit bond yields becoming lower than the interest rate on cash or reserves. 5

6 Contribution (cont.) Propose an efficient and accurate solution method able to apply to both the Black model and the Extended model. Show that the Extended model is superior to the Gaussian affine model and the Black model by estimation results using government bond term structure data from Switzerland, Germany and Japan. Quantify each effect of forward guidance, quantitative easing and the negative policy interest rate. Find that the power of arbitrage between money or reserves and government bonds moves in tandem with basis swap spreads. 6

7 Model i t = s t 1 {st y t } + {φ t s t + (1 φ t )y t }1 {st <y t } s t = ρx t Q dx t = κ x (θ x x t )dt + σ x dw x,t Q dy t = σ y dw y,t φ t = φ t 1 {0 φt 1} + 1 {1 φt }, dφ t = σ φ dw Q φ,t. λ t = λ 0 + λ 1 x t dw t P = λ t dt + dw t Q 7

8 Figure 1: Relationship between the nominal short rate and shadow rate Gaussian affine model Nominal short rate 45 Black model Nominal short rate Shadow rate Extended model Nominal short rate 45 Shadow rate 45 Shadow rate 8

9 Figure 2: Cumulative probability distribution function of nominal short rate Extended Model φ=0.1 Extended Model φ=0.5 Extended Model φ=0.9 Black Gaussian Affine Note: one-factor model, s t = 0, y t = 0, E t [s τ ] = 0.01,Var t [s τ ] =

10 Approximation methods Government bond price, P τ, and yield, R τ, at maturity τ τ P τ E Q [exp ( i t dt)], 0 R τ log(p τ )/τ. Priebsch (2013): 2nd order approximation of bond yields; R τ 1 τ τ (EQ [ i t dt 0 τ ] 0.5Var Q [ i t dt 0 ]), 10

11 Approximation methods (cont.) New approximation method I τ I τ α 0 + α 1 i1 4 τ + α 2i3 4 τ, P τ E Q [exp( I )]. τ R τ log(e Q [exp( I )])/τ, τ The parameters α 0 α 1 α 2 are determined by minimizing the mean squared error as follows; s. t. min E Q [(I τ I ) 2 τ ] E Q [I τ ] = E Q [I ], τ Var Q [I τ ] = Var Q [I ]. τ 11

12 Approximation methods (cont.) Distribution of I τ /τ and its approximations True Ueno Priebsch % -4% -2% 0% 2% 4% 6% 8% 10% Note: one-factor model, x 0 = 0, y = 0, θ = 0.01 κ = 0.1 σ = 0.2 φ = 0. Maturity is 10 year. 100,000 paths are generated. 12

13 Approximation methods (cont.) Maturity Shadow rate 1Y 5Y 10Y 30Y Exat Priebsch(2013) Rate of deviation % % % % 1% difference bps This paper Rate of deviation % % % % difference bps % Exact Priebsch(2013) Rate of deviation % % % % difference bps This paper Rate of deviation % % % % difference bps Note: one-factor model, y = 0, θ = 0.01 κ = 0.1 σ = 0.2 φ = 0. 13

14 Data Switzerland 3M 10% 1.5% 6M 8% 1.0% 1Y 6% 0.5% 2Y 3Y 5Y 4% 2% -0.5% 7Y 0% -1.0% 10Y -2% 12/1 13/1 14/1 15/1 16/1-1.5% Source: Bloomberg 14

15 Data (cont.) Germany 3M 6M 1Y 2Y 3Y 5Y 7Y 10Y 10% 8% 6% 4% 2% 0% -2% 12/1 13/1 14/1 15/1 16/1 2.5% 2.0% 1.5% 1.0% 0.5% -0.5% -1.0% Source: Bloomberg 15

16 Data (cont.) Japan 3M 6M 1Y 2Y 3Y 5Y 7Y 10Y 10% 8% 6% 4% 2% 0% 1.5% 1.0% 0.5% -2% 12/1 13/1 14/1 15/1 16/1-0.5% Source: Bloomberg 16

17 Estimation method Estimate four kinds of models by (quasi-) maximum likelihood estimation; the Gaussian affine model, the Black model, two versions of the Extended model. The difference between the two versions is whether φ t is constant or variable. Use the Single-Stage Iteration Filter (SSIF) for the Black model and Extended model and the Kalman filter for the Gaussian affine model as in Joslin et al. (2011) and others. In the Black model and Extended model, the relationships between factors and bond yields are not linear, so non-linear filtering method should be used. The Extended Kalman filter is used in many studies (Xia and Wu (2016) and others). Tanizaki (1996), however, shows by Monte Carlo simulations that estimation biases arise in the Extended Kalman filter if there is high non-linearity in estimated systems and propose the usage of other non-linear filtering methods including SSIF. 17

18 Estimation results: Parameters Gaussian affine Switzerland Germany Japan Black Extended Fixed Extended Variable Gaussian affine Black Extended Fixed Extended Variable Gaussian affine Black Extended Fixed Extended Variable φ σ φ Average of log likelihood P-value ( VS. Extended Fixed ) Pseudo P-value ( VS. Extended Variable ) T

19 Estimation results: RMSE Switzerland bps 3M 6M 1Y 2Y 3Y 5Y 7Y 10Y Average Gaussian affine Black Extended Fixed ExtendedVariable Germany bps 3M 6M 1Y 2Y 3Y 5Y 7Y 10Y Average Gaussian Affine Black Extended Fixed ExtendedVariable Japan bps 3M 6M 1Y 2Y 3Y 5Y 7Y 10Y Average Gaussian Affine Black Extended Fixed ExtendedVariable

20 Estimation results: Volatility Gaussian affine Switzerland Extended Variable 1.2 % 1.2 % M 6M 1Y 2Y 3Y 5Y 7Y 10Y 0.0 3M 6M 1Y 2Y 3Y 5Y 7Y 10Y Data during positive interest Data during zero interest Data during negative interest Model during positive interest Model during zero interest Model during negative interest 20

21 Estimation results: Volatility (cont.) Gaussian affine Germany Extended Variable 0.9 % 0.9 % M 6M 1Y 2Y 3Y 5Y 7Y 10Y 0.0 3M 6M 1Y 2Y 3Y 5Y 7Y 10Y Data during positive interest Data during zero interest Data during negative interest Model during positive interest Model during zero interest Model during negative interest 21

22 Estimation results: Volatility (cont.) Japan 0.9 % Gaussian affine 0.9 % Extended Variable M 6M 1Y 2Y 3Y 5Y 7Y 10Y 0.0 3M 6M 1Y 2Y 3Y 5Y 7Y 10Y Data during positive interest Data during zero interest Data during negative interest Model during positive interest Model during zero interest Model during negative interest 22

23 Estimation results: 10 year expected rate and term premium (cont.) Switzerland 10% 9% Term Premium Expected Rate 8% 7% 6% Market Rate Shadow Rate 5% 4% 3% 2% 1% 0% -1% -2% 89/1 91/1 93/1 95/1 97/1 99/1 01/1 03/1 05/1 07/1 09/1 11/1 13/1 15/1 23

24 Estimation results: 10 year expected rate and term premium (cont.) Germany 10% 9% Term Premium Expected Rate 8% 7% Market Rate Shadow Rate 6% 5% 4% 3% 2% 1% 0% -1% 91/10 93/10 95/10 97/10 99/10 01/10 03/10 05/10 07/10 09/10 11/10 13/10 15/10 24

25 Estimation results: 10 year expected rate and term premium (cont.) Japan 9% 8% 7% Term Premium Expected Rate 6% 5% Market Rate Shadow Rate 4% 3% 2% 1% 0% -1% -2% -3% -4% 89/4 91/4 93/4 95/4 97/4 99/4 01/4 03/4 05/4 07/4 09/4 11/4 13/4 15/4 25

26 Sensitivity of yield curves to the IOER Simple Example: E[i t ] = E[s t 1 {st y}] + y P(s t < y) 1.0 P(s t < y) E[s t ] = 0.0 E[s t + ] = E[s t 1 st 1 ] =0 E[s t ] = 0.01 E[s t ] = 0.00 E[s t 1 st 1 ] = 0.00 IOER reduction E[i t ] y = 0 y = 1 Diff. E[s t ] = % -0.20% -0.60%P E[s t ] = 0.10% -0.85% -0.95%P

27 Sensitivity of yield curves to the negative interest rate policy (cont.) Switzerland 2014/ /6 2016/6 3M 6M 1Y 2Y 3Y 5Y 7Y 10Y Germany 2010/6 2011/ /6 3M 6M 1Y 2Y 3Y 5Y 7Y 10Y 2014/ /6-0.5% /6-1.0% / /12-1.1% /6-1.0%

28 Sensitivity of yield curves to the negative interest rate policy (cont.) Japan /6 2012/1 2016/6 3M 6M 1Y 2Y 3Y 5Y 7Y 10Y 2009/ /1-1.5% /6-3.7%

29 Relationship between quantitative easing and yield term premia: Switzerland 2Y 0.8% 0.6% 0.4% 0.2% -0.2% -0.4% Term Premium SNB total asset, CHF billion, RHS -0.6% 10/1 11/1 12/1 13/1 14/1 15/1 16/ % 0.6% 0.4% 0.2% -0.2% -0.4% Term Premium SNB securities, CHF billion, RHS -0.6% 10/1 11/1 12/1 13/1 14/1 15/1 16/ Y 1.6% 1.4% 1.2% 1.0% 0.8% 0.6% 0.4% 0.2% -0.2% -0.4% -0.6% -0.8% -1.0% -1.2% -1.4% Term Premium SNB total asset, CHF billion, RHS 10/1 11/1 12/1 13/1 14/1 15/1 16/ % 1.4% 1.2% 1.0% 0.8% 0.6% 0.4% 0.2% -0.2% -0.4% -0.6% -0.8% -1.0% -1.2% -1.4% Term Premium SNB securities, CHF billion, RHS 10/1 11/1 12/1 13/1 14/1 15/1 16/

30 Relationship between quantitative easing and yield term premia: Germany 2Y 0.6% Term Premium % Term Premium % ECB total asset, EUR billion, RHS % ECB Securities held for monetary policy purposes, EUR billion, RHS % 0.2% % % % 10/1 11/1 12/1 13/1 14/1 15/1 16/ % 10/1 11/1 12/1 13/1 14/1 15/1 16/1 10Y 1.5% 1.0% 0.5% -0.5% Term Premium ECB total asset, EUR billion, RHS -1.0% 10/1 11/1 12/1 13/1 14/1 15/1 16/ % 1.0% 0.5% -0.5% Term Premium ECB Securities held for monetary policy purposes, EUR billion, RHS -1.0% 10/1 11/1 12/1 13/1 14/1 15/1 16/

31 Relationship between quantitative easing and yield term premia: Japan 2Y 0.04% 0.03% 0.02% 0.01% 0.00% -0.01% -0.02% Term Premium BOJ total asset, JPY trillion, RHS -0.03% 10/1 11/1 12/1 13/1 14/1 15/1 16/ % 0.03% 0.02% 0.01% 0.00% -0.01% -0.02% Term Premium BOJ Government Bond, JPY trillion, RHS -0.03% 10/1 11/1 12/1 13/1 14/1 15/1 16/ Y 0.9% 0 0.9% 0 0.8% 0.7% 0.6% % 0.7% 0.6% % 0.4% % 0.4% % 0.3% % 0.1% -0.1% -0.2% Term Premium BOJ total asset, JPY trillion, RHS % 0.1% -0.1% -0.2% Term Premium BOJ Government Bond, JPY trillion, RHS % 10/1 11/1 12/1 13/1 14/1 15/1 16/ % 10/1 11/1 12/1 13/1 14/1 15/1 16/

32 Decomposition of the yield curves R τ log(p τ )/τ log (EQ τ [exp( i(x t, y t, φ t )dt)]) 0 τ f Q (x t, y t, φ t ) τ = E P [ i(x t, 0, φ t )dt 0 +{f Q (x t, y t, φ t ) f Q (x t, 0, φ t )}. τ ] + {f Q (x t, 0, φ t ) E P [ i(x t, 0, φ t )dt 0 ]} 32

33 Decomposition of the yield curves: Switzerland 2Y 10Y 0.4% 1.5% 0.2% 1.0% 0.5% -0.2% -0.4% -0.6% -0.5% -0.8% term premium -1.0% -1.0% -1.2% expectation part ioer effect 14/1 14/4 14/7 14/10 15/1 15/4 15/7 15/10 16/1 16/4-1.5% -2.0% term premium expectation part ioer effect 14/1 14/4 14/7 14/10 15/1 15/4 15/7 15/10 16/1 16/4 33

34 Decomposition of the yield curves: Germany 2Y 10Y 0.3% 0.2% 0.1% -0.1% 2.0% 1.5% 1.0% term premium expectation part ioer effect -0.2% -0.3% 0.5% -0.4% term premium -0.5% -0.6% expectation part ioer effect -0.5% -0.7% 14/1 14/4 14/7 14/10 15/1 15/4 15/7 15/10 16/1 16/4-1.0% 14/1 14/4 14/7 14/10 15/1 15/4 15/7 15/10 16/1 16/4 34

35 Decomposition of the yield curves: Japan 2Y 10Y 0.15% 0.10% 0.05% 0.00% -0.05% 1.0% 0.9% 0.8% 0.7% 0.6% 0.5% 0.4% term premium expectation part ioer effect -0.10% -0.15% -0.20% term premium expectation part 0.3% 0.2% 0.1% -0.25% ioer effect -0.30% 12/1 12/7 13/1 13/7 14/1 14/7 15/1 15/7 16/1-0.1% -0.2% -0.3% 12/1 12/7 13/1 13/7 14/1 14/7 15/1 15/7 16/1 35

36 What is behind the movements of the power of arbitrage? φ 10Y CHFUSD Basis Swap (RHS) -0.9% -0.8% -0.7% -0.6% -0.5% -0.4% -0.3% -0.2% φ 10Y EURUSD Basis Swap (RHS) -0.6% -0.5% -0.4% -0.3% -0.2% -0.1% /9 12/9 13/9 14/9 15/9-0.1% /9 12/9 13/9 14/9 15/9 0.1% φ 1Y JPYEUR Basis Swap (RHS) -0.4% -0.3% -0.2% -0.1% % -0.6% -0.4% -0.2% /1 05/1 07/1 09/1 11/1 13/1 15/1 0.1% 0.2% 0.3% 0.4% φ 1Y JPYUSD Basis Swap (RHS) /1 05/1 07/1 09/1 11/1 13/1 15/1 0.2% 0.4% 36

37 A cross-currency basis swap A cross-currency basis swap is an agreement between two counterparties trading floating rate payments in their respective currencies. Without frictions in financial markets, a cross-currency swap should have a zero value with no spread on either side. But, there are relative funding costs in the different currencies over the lifetime of the swap. The market is charging a premium for transferring assets or liabilities from one currency to another. The cost is reflected as a spread on the floating leg in the foreign currency. U.S. investors can convert the cash flows from foreign government bonds in foreign currency to those in U.S. dollar through the basis swap market receiving premia. Even if the foreign government bond yields are negative, the large enough basis swap spreads can attract U.S. investors to investing the foreign government bonds. 37

38 Conclusion Develop a model to evaluate the effects of unconventional monetary policy measures including the negative interest rate policy on government bond term structures. Propose an efficient and accurate solution method applicable to both the Black model and the Extended model. Show that the Extended model is superior to the other models using data from Switzerland, Germany and Japan. Quantify each effect of FG, QE and the NIRP. Find that the power of arbitrage between money or reserves and government bonds moves in tandem with basis swap spreads. A two country term structure model is to be invented and empirically examined in future research. 38

Modeling Yields at the Zero Lower Bound: Are Shadow Rates the Solution?

Modeling Yields at the Zero Lower Bound: Are Shadow Rates the Solution? Modeling Yields at the Zero Lower Bound: Are Shadow Rates the Solution? Jens H. E. Christensen & Glenn D. Rudebusch Federal Reserve Bank of San Francisco Term Structure Modeling and the Lower Bound Problem

More information

Transmission of Quantitative Easing: The Role of Central Bank Reserves

Transmission of Quantitative Easing: The Role of Central Bank Reserves 1 / 1 Transmission of Quantitative Easing: The Role of Central Bank Reserves Jens H. E. Christensen & Signe Krogstrup 5th Conference on Fixed Income Markets Bank of Canada and Federal Reserve Bank of San

More information

Tomi Kortela. A Shadow rate model with timevarying lower bound of interest rates

Tomi Kortela. A Shadow rate model with timevarying lower bound of interest rates Tomi Kortela A Shadow rate model with timevarying lower bound of interest rates Bank of Finland Research Discussion Paper 19 2016 A Shadow rate model with time-varying lower bound of interest rates Tomi

More information

Interest rate models and Solvency II

Interest rate models and Solvency II www.nr.no Outline Desired properties of interest rate models in a Solvency II setting. A review of three well-known interest rate models A real example from a Norwegian insurance company 2 Interest rate

More information

Interest Rate Bermudan Swaption Valuation and Risk

Interest Rate Bermudan Swaption Valuation and Risk Interest Rate Bermudan Swaption Valuation and Risk Dmitry Popov FinPricing http://www.finpricing.com Summary Bermudan Swaption Definition Bermudan Swaption Payoffs Valuation Model Selection Criteria LGM

More information

Predictability of Interest Rates and Interest-Rate Portfolios

Predictability of Interest Rates and Interest-Rate Portfolios Predictability of Interest Rates and Interest-Rate Portfolios Liuren Wu Zicklin School of Business, Baruch College Joint work with Turan Bali and Massoud Heidari July 7, 2007 The Bank of Canada - Rotman

More information

Counterparty Credit Risk Simulation

Counterparty Credit Risk Simulation Counterparty Credit Risk Simulation Alex Yang FinPricing http://www.finpricing.com Summary Counterparty Credit Risk Definition Counterparty Credit Risk Measures Monte Carlo Simulation Interest Rate Curve

More information

A Macro-Finance Model of the Term Structure: the Case for a Quadratic Yield Model

A Macro-Finance Model of the Term Structure: the Case for a Quadratic Yield Model Title page Outline A Macro-Finance Model of the Term Structure: the Case for a 21, June Czech National Bank Structure of the presentation Title page Outline Structure of the presentation: Model Formulation

More information

Linear-Rational Term-Structure Models

Linear-Rational Term-Structure Models Linear-Rational Term-Structure Models Anders Trolle (joint with Damir Filipović and Martin Larsson) Ecole Polytechnique Fédérale de Lausanne Swiss Finance Institute AMaMeF and Swissquote Conference, September

More information

Interest Rate Cancelable Swap Valuation and Risk

Interest Rate Cancelable Swap Valuation and Risk Interest Rate Cancelable Swap Valuation and Risk Dmitry Popov FinPricing http://www.finpricing.com Summary Cancelable Swap Definition Bermudan Swaption Payoffs Valuation Model Selection Criteria LGM Model

More information

Market Price of Longevity Risk for A Multi-Cohort Mortality Model with Application to Longevity Bond Option Pricing

Market Price of Longevity Risk for A Multi-Cohort Mortality Model with Application to Longevity Bond Option Pricing 1/51 Market Price of Longevity Risk for A Multi-Cohort Mortality Model with Application to Longevity Bond Option Pricing Yajing Xu, Michael Sherris and Jonathan Ziveyi School of Risk & Actuarial Studies,

More information

Credit Valuation Adjustment and Funding Valuation Adjustment

Credit Valuation Adjustment and Funding Valuation Adjustment Credit Valuation Adjustment and Funding Valuation Adjustment Alex Yang FinPricing http://www.finpricing.com Summary Credit Valuation Adjustment (CVA) Definition Funding Valuation Adjustment (FVA) Definition

More information

Financial Risk Management

Financial Risk Management Financial Risk Management Professor: Thierry Roncalli Evry University Assistant: Enareta Kurtbegu Evry University Tutorial exercices #4 1 Correlation and copulas 1. The bivariate Gaussian copula is given

More information

A Multifrequency Theory of the Interest Rate Term Structure

A Multifrequency Theory of the Interest Rate Term Structure A Multifrequency Theory of the Interest Rate Term Structure Laurent Calvet, Adlai Fisher, and Liuren Wu HEC, UBC, & Baruch College Chicago University February 26, 2010 Liuren Wu (Baruch) Cascade Dynamics

More information

TopQuants. Integration of Credit Risk and Interest Rate Risk in the Banking Book

TopQuants. Integration of Credit Risk and Interest Rate Risk in the Banking Book TopQuants Integration of Credit Risk and Interest Rate Risk in the Banking Book 1 Table of Contents 1. Introduction 2. Proposed Case 3. Quantifying Our Case 4. Aggregated Approach 5. Integrated Approach

More information

Introduction to Financial Mathematics

Introduction to Financial Mathematics Department of Mathematics University of Michigan November 7, 2008 My Information E-mail address: marymorj (at) umich.edu Financial work experience includes 2 years in public finance investment banking

More information

Multi-Curve Pricing of Non-Standard Tenor Vanilla Options in QuantLib. Sebastian Schlenkrich QuantLib User Meeting, Düsseldorf, December 1, 2015

Multi-Curve Pricing of Non-Standard Tenor Vanilla Options in QuantLib. Sebastian Schlenkrich QuantLib User Meeting, Düsseldorf, December 1, 2015 Multi-Curve Pricing of Non-Standard Tenor Vanilla Options in QuantLib Sebastian Schlenkrich QuantLib User Meeting, Düsseldorf, December 1, 2015 d-fine d-fine All rights All rights reserved reserved 0 Swaption

More information

Callable Bond and Vaulation

Callable Bond and Vaulation and Vaulation Dmitry Popov FinPricing http://www.finpricing.com Summary Callable Bond Definition The Advantages of Callable Bonds Callable Bond Payoffs Valuation Model Selection Criteria LGM Model LGM

More information

Financial Risk Management

Financial Risk Management Financial Risk Management Professor: Thierry Roncalli Evry University Assistant: Enareta Kurtbegu Evry University Tutorial exercices #3 1 Maximum likelihood of the exponential distribution 1. We assume

More information

Puttable Bond and Vaulation

Puttable Bond and Vaulation and Vaulation Dmitry Popov FinPricing http://www.finpricing.com Summary Puttable Bond Definition The Advantages of Puttable Bonds Puttable Bond Payoffs Valuation Model Selection Criteria LGM Model LGM

More information

European spreads at the interest rate lower bound

European spreads at the interest rate lower bound European spreads at the interest rate lower bound Laura Coroneo University of York Sergio Pastorello University of Bologna First draft: 26th May 2017 Abstract This paper analyzes the effect of the interest

More information

Managing Systematic Mortality Risk in Life Annuities: An Application of Longevity Derivatives

Managing Systematic Mortality Risk in Life Annuities: An Application of Longevity Derivatives Managing Systematic Mortality Risk in Life Annuities: An Application of Longevity Derivatives Simon Man Chung Fung, Katja Ignatieva and Michael Sherris School of Risk & Actuarial Studies University of

More information

Estimation of dynamic term structure models

Estimation of dynamic term structure models Estimation of dynamic term structure models Greg Duffee Haas School of Business, UC-Berkeley Joint with Richard Stanton, Haas School Presentation at IMA Workshop, May 2004 (full paper at http://faculty.haas.berkeley.edu/duffee)

More information

Decomposing swap spreads

Decomposing swap spreads Decomposing swap spreads Peter Feldhütter Copenhagen Business School David Lando Copenhagen Business School (visiting Princeton University) Stanford, Financial Mathematics Seminar March 3, 2006 1 Recall

More information

LIBOR models, multi-curve extensions, and the pricing of callable structured derivatives

LIBOR models, multi-curve extensions, and the pricing of callable structured derivatives Weierstrass Institute for Applied Analysis and Stochastics LIBOR models, multi-curve extensions, and the pricing of callable structured derivatives John Schoenmakers 9th Summer School in Mathematical Finance

More information

Forecasting Interest Rates and Exchange Rates under Multi-Currency Quadratic Models

Forecasting Interest Rates and Exchange Rates under Multi-Currency Quadratic Models Forecasting Interest Rates and Exchange Rates under Multi-Currency Quadratic Models Markus Leippold Swiss Banking Institute, University of Zurich Liuren Wu Graduate School of Business, Fordham University

More information

ESGs: Spoilt for choice or no alternatives?

ESGs: Spoilt for choice or no alternatives? ESGs: Spoilt for choice or no alternatives? FA L K T S C H I R S C H N I T Z ( F I N M A ) 1 0 3. M i t g l i e d e r v e r s a m m l u n g S AV A F I R, 3 1. A u g u s t 2 0 1 2 Agenda 1. Why do we need

More information

Heterogeneous Firm, Financial Market Integration and International Risk Sharing

Heterogeneous Firm, Financial Market Integration and International Risk Sharing Heterogeneous Firm, Financial Market Integration and International Risk Sharing Ming-Jen Chang, Shikuan Chen and Yen-Chen Wu National DongHwa University Thursday 22 nd November 2018 Department of Economics,

More information

Understanding and Influencing the Yield Curve at the Zero Lower Bound

Understanding and Influencing the Yield Curve at the Zero Lower Bound Understanding and Influencing the Yield Curve at the Zero Lower Bound Glenn D. Rudebusch Federal Reserve Bank of San Francisco September 9, 2014 European Central Bank and Bank of England workshop European

More information

Market interest-rate models

Market interest-rate models Market interest-rate models Marco Marchioro www.marchioro.org November 24 th, 2012 Market interest-rate models 1 Lecture Summary No-arbitrage models Detailed example: Hull-White Monte Carlo simulations

More information

From default probabilities to credit spreads: Credit risk models do explain market prices

From default probabilities to credit spreads: Credit risk models do explain market prices From default probabilities to credit spreads: Credit risk models do explain market prices Presented by Michel M Dacorogna (Joint work with Stefan Denzler, Alexander McNeil and Ulrich A. Müller) The 2007

More information

Advances in Valuation Adjustments. Topquants Autumn 2015

Advances in Valuation Adjustments. Topquants Autumn 2015 Advances in Valuation Adjustments Topquants Autumn 2015 Quantitative Advisory Services EY QAS team Modelling methodology design and model build Methodology and model validation Methodology and model optimisation

More information

Investors Attention and Stock Market Volatility

Investors Attention and Stock Market Volatility Investors Attention and Stock Market Volatility Daniel Andrei Michael Hasler Princeton Workshop, Lausanne 2011 Attention and Volatility Andrei and Hasler Princeton Workshop 2011 0 / 15 Prerequisites Attention

More information

Pricing Pension Buy-ins and Buy-outs 1

Pricing Pension Buy-ins and Buy-outs 1 Pricing Pension Buy-ins and Buy-outs 1 Tianxiang Shi Department of Finance College of Business Administration University of Nebraska-Lincoln Longevity 10, Santiago, Chile September 3-4, 2014 1 Joint work

More information

Introduction. Practitioner Course: Interest Rate Models. John Dodson. February 18, 2009

Introduction. Practitioner Course: Interest Rate Models. John Dodson. February 18, 2009 Practitioner Course: Interest Rate Models February 18, 2009 syllabus text sessions office hours date subject reading 18 Feb introduction BM 1 25 Feb affine models BM 3 4 Mar Gaussian models BM 4 11 Mar

More information

Pricing Variance Swaps under Stochastic Volatility Model with Regime Switching - Discrete Observations Case

Pricing Variance Swaps under Stochastic Volatility Model with Regime Switching - Discrete Observations Case Pricing Variance Swaps under Stochastic Volatility Model with Regime Switching - Discrete Observations Case Guang-Hua Lian Collaboration with Robert Elliott University of Adelaide Feb. 2, 2011 Robert Elliott,

More information

Rue de la Banque No. 52 November 2017

Rue de la Banque No. 52 November 2017 Staying at zero with affine processes: an application to term structure modelling Alain Monfort Banque de France and CREST Fulvio Pegoraro Banque de France, ECB and CREST Jean-Paul Renne HEC Lausanne Guillaume

More information

Time-Varying Lower Bound of Interest Rates in Europe

Time-Varying Lower Bound of Interest Rates in Europe Time-Varying Lower Bound of Interest Rates in Europe Jing Cynthia Wu Chicago Booth and NBER Fan Dora Xia Bank for International Settlements First draft: January 17, 2017 This draft: February 13, 2017 Abstract

More information

Analysis of the Models Used in Variance Swap Pricing

Analysis of the Models Used in Variance Swap Pricing Analysis of the Models Used in Variance Swap Pricing Jason Vinar U of MN Workshop 2011 Workshop Goals Price variance swaps using a common rule of thumb used by traders, using Monte Carlo simulation with

More information

Earnings Inequality and the Minimum Wage: Evidence from Brazil

Earnings Inequality and the Minimum Wage: Evidence from Brazil Earnings Inequality and the Minimum Wage: Evidence from Brazil Niklas Engbom June 16, 2016 Christian Moser World Bank-Bank of Spain Conference This project Shed light on drivers of earnings inequality

More information

Robust Optimization Applied to a Currency Portfolio

Robust Optimization Applied to a Currency Portfolio Robust Optimization Applied to a Currency Portfolio R. Fonseca, S. Zymler, W. Wiesemann, B. Rustem Workshop on Numerical Methods and Optimization in Finance June, 2009 OUTLINE Introduction Motivation &

More information

Portfolio Credit Risk II

Portfolio Credit Risk II University of Toronto Department of Mathematics Department of Mathematical Finance July 31, 2011 Table of Contents 1 A Worked-Out Example Expected Loss Unexpected Loss Credit Reserve 2 Examples Problem

More information

Discussion of No-Arbitrage Near-Cointegrated VAR(p) Term Structure Models, Term Premia and GDP Growth by C. Jardet, A. Monfort and F.

Discussion of No-Arbitrage Near-Cointegrated VAR(p) Term Structure Models, Term Premia and GDP Growth by C. Jardet, A. Monfort and F. Discussion of No-Arbitrage Near-Cointegrated VAR(p) Term Structure Models, Term Premia and GDP Growth by C. Jardet, A. Monfort and F. Pegoraro R. Mark Reesor Department of Applied Mathematics The University

More information

dt + ρσ 2 1 ρ2 σ 2 B i (τ) = 1 e κ iτ κ i

dt + ρσ 2 1 ρ2 σ 2 B i (τ) = 1 e κ iτ κ i A 2D Gaussian model (akin to Brigo & Mercurio Section 4.2) Suppose where dx(t) = ( κ1 0 0 κ 2 ) ( X1 (t) X 2 (t) In this case we find (BLACKBOARD) that r(t) = δ 0 + X 1 (t) + X 2 (t) ) ( σ1 0 dt + ρσ 2

More information

Chapter 6 Forecasting Volatility using Stochastic Volatility Model

Chapter 6 Forecasting Volatility using Stochastic Volatility Model Chapter 6 Forecasting Volatility using Stochastic Volatility Model Chapter 6 Forecasting Volatility using SV Model In this chapter, the empirical performance of GARCH(1,1), GARCH-KF and SV models from

More information

Understanding the Death Benefit Switch Option in Universal Life Policies

Understanding the Death Benefit Switch Option in Universal Life Policies 1 Understanding the Death Benefit Switch Option in Universal Life Policies Nadine Gatzert, University of Erlangen-Nürnberg Gudrun Hoermann, Munich 2 Motivation Universal life policies are the most popular

More information

Dollar Funding of Global banks and Regulatory Reforms: Evidence from the Impact of Monetary Policy Divergence

Dollar Funding of Global banks and Regulatory Reforms: Evidence from the Impact of Monetary Policy Divergence Dollar Funding of Global banks and Regulatory Reforms: Evidence from the Impact of Monetary Policy Divergence Nao Sudo Monetary Affairs Department Bank of Japan Prepared for Symposium: CIP-RIP? at Bank

More information

The Use of Importance Sampling to Speed Up Stochastic Volatility Simulations

The Use of Importance Sampling to Speed Up Stochastic Volatility Simulations The Use of Importance Sampling to Speed Up Stochastic Volatility Simulations Stan Stilger June 6, 1 Fouque and Tullie use importance sampling for variance reduction in stochastic volatility simulations.

More information

European option pricing under parameter uncertainty

European option pricing under parameter uncertainty European option pricing under parameter uncertainty Martin Jönsson (joint work with Samuel Cohen) University of Oxford Workshop on BSDEs, SPDEs and their Applications July 4, 2017 Introduction 2/29 Introduction

More information

Vayanos and Vila, A Preferred-Habitat Model of the Term Stru. the Term Structure of Interest Rates

Vayanos and Vila, A Preferred-Habitat Model of the Term Stru. the Term Structure of Interest Rates Vayanos and Vila, A Preferred-Habitat Model of the Term Structure of Interest Rates December 4, 2007 Overview Term-structure model in which investers with preferences for specific maturities and arbitrageurs

More information

Estimating Term Premia at the Zero

Estimating Term Premia at the Zero Bank of Japan Working Paper Series Estimating Term Premia at the Zero Bound: An Analysis of Japanese, US, and UK Yields Hibiki Ichiue * hibiki.ichiue@boj.or.jp Yoichi Ueno ** youichi.ueno@boj.or.jp No.13-E-8

More information

Supplementary Appendix to The Risk Premia Embedded in Index Options

Supplementary Appendix to The Risk Premia Embedded in Index Options Supplementary Appendix to The Risk Premia Embedded in Index Options Torben G. Andersen Nicola Fusari Viktor Todorov December 214 Contents A The Non-Linear Factor Structure of Option Surfaces 2 B Additional

More information

Linearity-Generating Processes, Unspanned Stochastic Volatility, and Interest-Rate Option Pricing

Linearity-Generating Processes, Unspanned Stochastic Volatility, and Interest-Rate Option Pricing Linearity-Generating Processes, Unspanned Stochastic Volatility, and Interest-Rate Option Pricing Liuren Wu, Baruch College Joint work with Peter Carr and Xavier Gabaix at New York University Board of

More information

Assessing Potential Inflation Consequences of QE after Financial Crises

Assessing Potential Inflation Consequences of QE after Financial Crises Assessing Potential Inflation Consequences of QE after Financial Crises Samuel Reynard Economic Advisor International dimensions of conventional and unconventional monetary policy ECB-IMF Conference, Frankfurt,

More information

Exploring Volatility Derivatives: New Advances in Modelling. Bruno Dupire Bloomberg L.P. NY

Exploring Volatility Derivatives: New Advances in Modelling. Bruno Dupire Bloomberg L.P. NY Exploring Volatility Derivatives: New Advances in Modelling Bruno Dupire Bloomberg L.P. NY bdupire@bloomberg.net Global Derivatives 2005, Paris May 25, 2005 1. Volatility Products Historical Volatility

More information

Value at Risk Ch.12. PAK Study Manual

Value at Risk Ch.12. PAK Study Manual Value at Risk Ch.12 Related Learning Objectives 3a) Apply and construct risk metrics to quantify major types of risk exposure such as market risk, credit risk, liquidity risk, regulatory risk etc., and

More information

Inflation risks and inflation risk premia

Inflation risks and inflation risk premia Inflation risks and inflation risk premia by Juan Angel Garcia and Thomas Werner Discussion by: James M Steeley, Aston Business School Conference on "The Yield Curve and New Developments in Macro-finance"

More information

Exact Sampling of Jump-Diffusion Processes

Exact Sampling of Jump-Diffusion Processes 1 Exact Sampling of Jump-Diffusion Processes and Dmitry Smelov Management Science & Engineering Stanford University Exact Sampling of Jump-Diffusion Processes 2 Jump-Diffusion Processes Ubiquitous in finance

More information

Polynomial Models in Finance

Polynomial Models in Finance Polynomial Models in Finance Martin Larsson Department of Mathematics, ETH Zürich based on joint work with Damir Filipović, Anders Trolle, Tony Ware Risk Day Zurich, 11 September 2015 Flexibility Tractability

More information

Risk Management. Exercises

Risk Management. Exercises Risk Management Exercises Exercise Value at Risk calculations Problem Consider a stock S valued at $1 today, which after one period can be worth S T : $2 or $0.50. Consider also a convertible bond B, which

More information

Matlab Based Stochastic Processes in Stochastic Asset Portfolio Optimization

Matlab Based Stochastic Processes in Stochastic Asset Portfolio Optimization Matlab Based Stochastic Processes in Stochastic Asset Portfolio Optimization Workshop OR und Statistische Analyse mit Mathematischen Tools, May 13th, 2014 Dr. Georg Ostermaier, Ömer Kuzugüden Agenda Introduction

More information

The Information Content of the Yield Curve

The Information Content of the Yield Curve The Information Content of the Yield Curve by HANS-JüRG BüTTLER Swiss National Bank and University of Zurich Switzerland 0 Introduction 1 Basic Relationships 2 The CIR Model 3 Estimation: Pooled Time-series

More information

Calculating VaR. There are several approaches for calculating the Value at Risk figure. The most popular are the

Calculating VaR. There are several approaches for calculating the Value at Risk figure. The most popular are the VaR Pro and Contra Pro: Easy to calculate and to understand. It is a common language of communication within the organizations as well as outside (e.g. regulators, auditors, shareholders). It is not really

More information

Credit Risk Management: A Primer. By A. V. Vedpuriswar

Credit Risk Management: A Primer. By A. V. Vedpuriswar Credit Risk Management: A Primer By A. V. Vedpuriswar February, 2019 Altman s Z Score Altman s Z score is a good example of a credit scoring tool based on data available in financial statements. It is

More information

State Space Estimation of Dynamic Term Structure Models with Forecasts

State Space Estimation of Dynamic Term Structure Models with Forecasts State Space Estimation of Dynamic Term Structure Models with Forecasts Liuren Wu November 19, 2015 Liuren Wu Estimation and Application November 19, 2015 1 / 39 Outline 1 General setting 2 State space

More information

dt+ ρσ 2 1 ρ2 σ 2 κ i and that A is a rather lengthy expression that we may or may not need. (Brigo & Mercurio Lemma Thm , p. 135.

dt+ ρσ 2 1 ρ2 σ 2 κ i and that A is a rather lengthy expression that we may or may not need. (Brigo & Mercurio Lemma Thm , p. 135. A 2D Gaussian model (akin to Brigo & Mercurio Section 4.2) Suppose where ( κ1 0 dx(t) = 0 κ 2 r(t) = δ 0 +X 1 (t)+x 2 (t) )( X1 (t) X 2 (t) ) ( σ1 0 dt+ ρσ 2 1 ρ2 σ 2 )( dw Q 1 (t) dw Q 2 (t) ) In this

More information

Negative Rates: The Challenges from a Quant Perspective

Negative Rates: The Challenges from a Quant Perspective Negative Rates: The Challenges from a Quant Perspective 1 Introduction Fabio Mercurio Global head of Quantitative Analytics Bloomberg There are many instances in the past and recent history where Treasury

More information

Monetary Policy Divergence and Global Financial Stability: From the Perspective of Demand and Supply of Safe Assets

Monetary Policy Divergence and Global Financial Stability: From the Perspective of Demand and Supply of Safe Assets Monetary Policy Divergence and Global Financial Stability: From the Perspective of Demand and Supply of Safe Assets January, 7 Speech at a Meeting Hosted by the International Bankers Association of Japan

More information

Making money in electricity markets

Making money in electricity markets Making money in electricity markets Risk-minimising hedging: from classic machinery to supervised learning Martin Tégner martin.tegner@eng.ox.ac.uk Department of Engineering Science & Oxford-Man Institute

More information

(J)CIR(++) Hazard Rate Model

(J)CIR(++) Hazard Rate Model (J)CIR(++) Hazard Rate Model Henning Segger - Quaternion Risk Management c 2013 Quaternion Risk Management Ltd. All Rights Reserved. 1 1 2 3 4 5 6 c 2013 Quaternion Risk Management Ltd. All Rights Reserved.

More information

Economic Scenario Generator: Applications in Enterprise Risk Management. Ping Sun Executive Director, Financial Engineering Numerix LLC

Economic Scenario Generator: Applications in Enterprise Risk Management. Ping Sun Executive Director, Financial Engineering Numerix LLC Economic Scenario Generator: Applications in Enterprise Risk Management Ping Sun Executive Director, Financial Engineering Numerix LLC Numerix makes no representation or warranties in relation to information

More information

Faster solutions for Black zero lower bound term structure models

Faster solutions for Black zero lower bound term structure models Crawford School of Public Policy CAMA Centre for Applied Macroeconomic Analysis Faster solutions for Black zero lower bound term structure models CAMA Working Paper 66/2013 September 2013 Leo Krippner

More information

ECON 815. A Basic New Keynesian Model II

ECON 815. A Basic New Keynesian Model II ECON 815 A Basic New Keynesian Model II Winter 2015 Queen s University ECON 815 1 Unemployment vs. Inflation 12 10 Unemployment 8 6 4 2 0 1 1.5 2 2.5 3 3.5 4 4.5 5 Core Inflation 14 12 10 Unemployment

More information

Optimal Search for Parameters in Monte Carlo Simulation for Derivative Pricing

Optimal Search for Parameters in Monte Carlo Simulation for Derivative Pricing Optimal Search for Parameters in Monte Carlo Simulation for Derivative Pricing Prof. Chuan-Ju Wang Department of Computer Science University of Taipei Joint work with Prof. Ming-Yang Kao March 28, 2014

More information

Optimal Hedging of Variance Derivatives. John Crosby. Centre for Economic and Financial Studies, Department of Economics, Glasgow University

Optimal Hedging of Variance Derivatives. John Crosby. Centre for Economic and Financial Studies, Department of Economics, Glasgow University Optimal Hedging of Variance Derivatives John Crosby Centre for Economic and Financial Studies, Department of Economics, Glasgow University Presentation at Baruch College, in New York, 16th November 2010

More information

IEOR E4703: Monte-Carlo Simulation

IEOR E4703: Monte-Carlo Simulation IEOR E4703: Monte-Carlo Simulation Simulating Stochastic Differential Equations Martin Haugh Department of Industrial Engineering and Operations Research Columbia University Email: martin.b.haugh@gmail.com

More information

FINANCE, INVESTMENT & RISK MANAGEMENT CONFERENCE. SWAPS and SWAPTIONS Interest Rate Risk Exposures JUNE 2008 HILTON DEANSGATE, MANCHESTER

FINANCE, INVESTMENT & RISK MANAGEMENT CONFERENCE. SWAPS and SWAPTIONS Interest Rate Risk Exposures JUNE 2008 HILTON DEANSGATE, MANCHESTER FINANCE, INVESTMENT & RISK MANAGEMENT CONFERENCE 5-7 JUNE 8 HILTON DEANSGATE, MANCHESTER SWAPS and SWAPTIONS Interest Rate Risk Eposures Viktor Mirkin vmirkin@deloitte.co.uk 7 JUNE 8 HILTON DEANSGATE,

More information

GLWB Guarantees: Hedge E ciency & Longevity Analysis

GLWB Guarantees: Hedge E ciency & Longevity Analysis GLWB Guarantees: Hedge E ciency & Longevity Analysis Etienne Marceau, Ph.D. A.S.A. (Full Prof. ULaval, Invited Prof. ISFA, Co-director Laboratoire ACT&RISK, LoLiTA) Pierre-Alexandre Veilleux, FSA, FICA,

More information

On modelling of electricity spot price

On modelling of electricity spot price , Rüdiger Kiesel and Fred Espen Benth Institute of Energy Trading and Financial Services University of Duisburg-Essen Centre of Mathematics for Applications, University of Oslo 25. August 2010 Introduction

More information

Investment strategies and risk management for participating life insurance contracts

Investment strategies and risk management for participating life insurance contracts 1/20 Investment strategies and risk for participating life insurance contracts and Steven Haberman Cass Business School AFIR Colloquium Munich, September 2009 2/20 & Motivation Motivation New supervisory

More information

Practical example of an Economic Scenario Generator

Practical example of an Economic Scenario Generator Practical example of an Economic Scenario Generator Martin Schenk Actuarial & Insurance Solutions SAV 7 March 2014 Agenda Introduction Deterministic vs. stochastic approach Mathematical model Application

More information

Fiscal Multipliers in Recessions. M. Canzoneri, F. Collard, H. Dellas and B. Diba

Fiscal Multipliers in Recessions. M. Canzoneri, F. Collard, H. Dellas and B. Diba 1 / 52 Fiscal Multipliers in Recessions M. Canzoneri, F. Collard, H. Dellas and B. Diba 2 / 52 Policy Practice Motivation Standard policy practice: Fiscal expansions during recessions as a means of stimulating

More information

Economic Scenario Generators

Economic Scenario Generators Economic Scenario Generators A regulator s perspective Falk Tschirschnitz, FINMA Bahnhofskolloquium Motivation FINMA has observed: Calibrating the interest rate model of choice has become increasingly

More information

Risk-Adjusted Capital Allocation and Misallocation

Risk-Adjusted Capital Allocation and Misallocation Risk-Adjusted Capital Allocation and Misallocation Joel M. David Lukas Schmid David Zeke USC Duke & CEPR USC Summer 2018 1 / 18 Introduction In an ideal world, all capital should be deployed to its most

More information

Statistical Inference and Methods

Statistical Inference and Methods Department of Mathematics Imperial College London d.stephens@imperial.ac.uk http://stats.ma.ic.ac.uk/ das01/ 14th February 2006 Part VII Session 7: Volatility Modelling Session 7: Volatility Modelling

More information

On VIX Futures in the rough Bergomi model

On VIX Futures in the rough Bergomi model On VIX Futures in the rough Bergomi model Oberwolfach Research Institute for Mathematics, February 28, 2017 joint work with Antoine Jacquier and Claude Martini Contents VIX future dynamics under rbergomi

More information

Managing Temperature Driven Volume Risks

Managing Temperature Driven Volume Risks Managing Temperature Driven Volume Risks Pascal Heider (*) E.ON Global Commodities SE 21. January 2015 (*) joint work with Laura Cucu, Rainer Döttling, Samuel Maina Contents 1 Introduction 2 Model 3 Calibration

More information

Model Risk Embedded in Yield-Curve Construction Methods

Model Risk Embedded in Yield-Curve Construction Methods Model Risk Embedded in Yield-Curve Construction Methods Areski Cousin ISFA, Université Lyon 1 Joint work with Ibrahima Niang Bachelier Congress 2014 Brussels, June 5, 2014 Areski Cousin, ISFA, Université

More information

The Crude Oil Futures Curve, the U.S. Term Structure and Global Macroeconomic Shocks

The Crude Oil Futures Curve, the U.S. Term Structure and Global Macroeconomic Shocks The Crude Oil Futures Curve, the U.S. Term Structure and Global Macroeconomic Shocks Ron Alquist Gregory H. Bauer Antonio Diez de los Rios Bank of Canada Bank of Canada Bank of Canada November 20, 2012

More information

American Option Pricing: A Simulated Approach

American Option Pricing: A Simulated Approach Utah State University DigitalCommons@USU All Graduate Plan B and other Reports Graduate Studies 5-2013 American Option Pricing: A Simulated Approach Garrett G. Smith Utah State University Follow this and

More information

Macro factors and sovereign bond spreads: aquadraticno-arbitragemodel

Macro factors and sovereign bond spreads: aquadraticno-arbitragemodel Macro factors and sovereign bond spreads: aquadraticno-arbitragemodel Peter Hˆrdahl a, Oreste Tristani b a Bank for International Settlements, b European Central Bank 17 December 1 All opinions are personal

More information

Reverse Sensitivity Testing: What does it take to break the model? Silvana Pesenti

Reverse Sensitivity Testing: What does it take to break the model? Silvana Pesenti Reverse Sensitivity Testing: What does it take to break the model? Silvana Pesenti Silvana.Pesenti@cass.city.ac.uk joint work with Pietro Millossovich and Andreas Tsanakas Insurance Data Science Conference,

More information

Risks For The Long Run And The Real Exchange Rate

Risks For The Long Run And The Real Exchange Rate Riccardo Colacito, Mariano M. Croce Overview International Equity Premium Puzzle Model with long-run risks Calibration Exercises Estimation Attempts & Proposed Extensions Discussion International Equity

More information

Introduction to credit risk

Introduction to credit risk Introduction to credit risk Marco Marchioro www.marchioro.org December 1 st, 2012 Introduction to credit derivatives 1 Lecture Summary Credit risk and z-spreads Risky yield curves Riskless yield curve

More information

Empirical Approach to the Heston Model Parameters on the Exchange Rate USD / COP

Empirical Approach to the Heston Model Parameters on the Exchange Rate USD / COP Empirical Approach to the Heston Model Parameters on the Exchange Rate USD / COP ICASQF 2016, Cartagena - Colombia C. Alexander Grajales 1 Santiago Medina 2 1 University of Antioquia, Colombia 2 Nacional

More information

Resource Allocation within Firms and Financial Market Dislocation: Evidence from Diversified Conglomerates

Resource Allocation within Firms and Financial Market Dislocation: Evidence from Diversified Conglomerates Resource Allocation within Firms and Financial Market Dislocation: Evidence from Diversified Conglomerates Gregor Matvos and Amit Seru (RFS, 2014) Corporate Finance - PhD Course 2017 Stefan Greppmair,

More information

Parametric Inference and Dynamic State Recovery from Option Panels. Torben G. Andersen

Parametric Inference and Dynamic State Recovery from Option Panels. Torben G. Andersen Parametric Inference and Dynamic State Recovery from Option Panels Torben G. Andersen Joint work with Nicola Fusari and Viktor Todorov The Third International Conference High-Frequency Data Analysis in

More information

M5MF6. Advanced Methods in Derivatives Pricing

M5MF6. Advanced Methods in Derivatives Pricing Course: Setter: M5MF6 Dr Antoine Jacquier MSc EXAMINATIONS IN MATHEMATICS AND FINANCE DEPARTMENT OF MATHEMATICS April 2016 M5MF6 Advanced Methods in Derivatives Pricing Setter s signature...........................................

More information

A New Class of Non-linear Term Structure Models. Discussion

A New Class of Non-linear Term Structure Models. Discussion A New Class of Non-linear Term Structure Models by Eraker, Wang and Wu Discussion Pietro Veronesi The University of Chicago Booth School of Business Main Contribution and Outline of Discussion Main contribution

More information

Interest Rate Models: An ALM Perspective Ser-Huang Poon Manchester Business School

Interest Rate Models: An ALM Perspective Ser-Huang Poon Manchester Business School Interest Rate Models: An ALM Perspective Ser-Huang Poon Manchester Business School 1 Interest Rate Models: An ALM Perspective (with NAG implementation) Ser-Huang Poon Manchester Business School Full paper:

More information