quan OPTIONS ANALYTICS IN REAL-TIME PROBLEM: Industry SOLUTION: Oquant Real-time Options Pricing

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1 OPTIONS ANALYTICS IN REAL-TIME A major aspect of Financial Mathematics is option pricing theory. Oquant provides real time option analytics in the cloud. We have developed a powerful system that utilizes our proprietary technology and mathematics to compute most reliable pricing data for American call and put options. We provide data on Equities, FOREX and Commodities. Our approach is a brand new analytical approximation that's 000 times faster than the binomial tree with 0,000 nodes, yet extremely accurate. Exhibits to provide detailed comparative analysis, we took many famous approximations. Tree with N = 0,000 (donating True Price ), MBAW a quadratic approximation by MacMillan and Barone-Adesi and Ju and Zhong's (JZ) modified quadratic approach along with Bjerksund-Stensland (BJST) were compared in great detail. Oquant (OQNT) approach is a breakthrough proprietary algorithm that's 000 times faster than the Tree mentioned above, provides major greeks at no extra time and yields highest accuracy compared to other analytical techniques. PROBLEM: Industry The European and American call and put options are "plain vanilla" financial instruments traded throughout the world. One can compare the actual options price with those based on the Black-Scholes model that involves the price of the underlying asset and the risk-free interest rate, which are directly observable, and the volatility σ of the asset s return, which has to be estimated from past data. Most common assumption for underlying assets is the lognormal diffusion (Black-Scholes) with constant parameters. Currently professionals rely on non analytical techniques such as the trinomial trees and partial differential equations (PDE), which are very time consuming, become even (up to 0 times) more tedious when greeks are computed, and end up being still inaccurate and unstable, especially the greeks. In terms of analytical approximations MBAW is the oldest, fastest but not always accurate, Ju-Zhong a modified quadratic technique doesn't produce strong results either and in many cases blows up. Lastly Bjerksund-Stenseland is rarely accurate due to simplistic assumptions about optimal exercise boundary. Providing a technique capable of solving direct and inverse problems of American options accurately in real-time still remains a challenge due to the absence of a powerful analytical approach addressing real time pricing of American options in a consistent way. Additionally, needs for further analytics such as the time-dependence (term structure) in parameters and discrete dividends are making the described set of systemic problems even more complicated. SOLUTION: Oquant Real-time Options Pricing We have developed and tested a more accurate analytical approximation, under the assumption of Black-Scholes with constant parameters. We offer an extremely fast method of pricing and repricing on a given set of implied volatilities and fast real time volatility implication at various strikes and maturities using the optimal exercise boundary. Furthermore, we provide many other type of analytics such as time-dependency and implications of discrete dividends. Our proprietary algorithms take a microseconds to compute option prices. Option traders want this but don t have the time or resources to get to it, because most professionals currently relying on much older approximations that are time consuming and inaccurate. Oquant aims to change this with its efficient real-time actionable option analytics. ADVANTAGES OF OQNT (Oquant): Efficient Analytical Approximation - Accurate and super fast at the same time - Minimal latency in both direct and inverse directions, instant re-computation (making it suitable for streaming, quoting, searching in real-time) - Internally and externally parallelizable, suitable for high intensity multi-client remote/distributed (cloud) services - Right choice for more accurate electronic market making - Available on web and mobile - Super-fast, accurate and stable Delta, Gamma and Theta - Dramatic time reduction in computing risks for portfolios containing a high number of American options - Many more options and financial instrument analytics such as the following: - Better estimate of long term underlying volatility as a function of time from listed American options - Estimation of unannounced discrete dividends from listed options at longer term maturities - More accurate estimates of volatility and dividends - better long term prediction of underlying assets

2 Options Data EXHIBIT 0 0 VALUES OF AMERICAN PUTS (S = $0, r = 0.0, d = 0.0) (K, σ, τ (yr)) (,0.,0.0) (,0.,0.) (,0.,0.) (0,0.,0.0) (0,0.,0.) (0,0.,0.) (,0.,0.0) (,0.,0.) (,0.,0.) (,0.,0.0) (,0.,0.) (,0.,0.) (0,0.,0.0) (0,0.,0.) (0,0.,0.) (,0.,0.0) (,0.,0.) (,0.,0.) (,0.,0.0) (,0.,0.) (,0.,0.) (0,0.,0.0) (0,0.,0.) (0,0.,0.) (,0.,0.0) (,0.,0.) (,0.,0.) VALUES OF AMERICAN CALLS (K= $00, τ = 0. (yr)) (0,0.,0.0,0.0) (0,0.,0.0,0.0) (00,0.,0.0,0.0) (0,0.,0.0,0.0) (0,0.,0.0,0.0) (0,0.,0.0,0.0) (0,0.,0.0,0.0) (00,0.,0.0,0.0) (0,0.,0.0,0.0) (0,0.,0.0,0.0) (0,0.,0.00,0.0) (0,0.,0.00,0.0) (00,0.,0.00,0.0) (0,0.,0.00,0.0) (0,0.,0.00,0.0) (0,0.,0.0,0.0) (0,0.,0.0,0.0) (00,0.,0.0,0.0) (0,0.,0.0,0.0) (0,0.,0.0,0.0) [] [] [] [] [] The TRUE value is based on binomial (TREE) with N = 0,000. Columns - represent the methods, Oquant approximation (prop mathematical algorithm), binomial and accelerated binomial with N = 0, MacMillan [] and Barone-Adesi and Whaley [] (MBAW), and the Ju and Zhong's [] modified (S, σ, r, d) [] [] [] [] [] The TRUE value is based on binomial (TREE) with N = 0,000. Columns - represent the methods, Oquant approximation (prop mathematical algorithm), binomial and accelerated binomial with N = 0, MacMillan [] and Barone-Adesi and Whaley [] (MBAW), and the Ju and Zhong's [] modified

3 q uan EXHIBIT 0 VALUES OF AMERICAN PUTS (K = $00, τ =.0 (yr), σ = 0., r = 0.0) (S, d) (0,0.) (0,0.) (00,0.) (0,0.) (0,0.) (0,0.0) (0,0.0) (00,0.0) (0,0.0) (0,0.0) (0,0.0) (0,0.0) (00,0.0) (0,0.0) (0,0.0) (0,0.0) (0,0.0) (00,0.0) (0,0.0) (0,0.0) [] [] [] [] [] The TRUE value is based on binomial (TREE) with N = 0,000. Columns - represent the methods, Oquant approximation (prop mathematical algorithm), binomial and accelerated binomial with N = 0, MacMillan [] and Barone-Adesi and Whaley [] (MBAW), and the Ju and Zhong's [] modified 0 VALUES OF AMERICAN CALLS (K= $00, τ =.0 (yr)) [] [] [] [] [] (S,σ, r, d) (0,0.,0.0,0.0) (0,0.,0.0,0.0) (00,0.,0.0,0.0) (0,0.,0.0,0.0) (0,0.,0.0,0.0) (0,0.,0.0,0.0) (0,0.,0.0,0.0) (00,0.,0.0,0.0) (0,0.,0.0,0.0) (0,0.,0.0,0.0) (0,0.,0.00,0.0) (0,0.,0.00,0.0) (00,0.,0.00,0.0) (0,0.,0.00,0.0) (0,0.,0.00,0.0) (0,0.,0.0,0.0) (0,0.,0.0,0.0) (00,0.,0.0,0.0) (0,0.,0.0,0.0) (0,0.,0.0,0.0) The TRUE value is based on binomial (TREE) with N = 0,000. Columns - represent the methods, Oquant approximation (prop mathematical algorithm), binomial and accelerated binomial with N = 0, MacMillan [] and Barone-Adesi and Whaley [] (MBAW), and the Ju and Zhong's [] modified

4 EXHIBIT Approx. option values. Strike K = 00, cost of carry b = -0:0 r = 0.0, σ = 0., T = r = 0., σ = 0., T = r = 0.0, σ = 0.0, T = r = 0.0, σ = 0., T = TREE: Binomial call and put approximation with points on the lattice. Bjerksund-Stensland [0] (BJST) :Two-step boundary call and put approximation. Approx. option values. Strike K = 00, cost of carry b = 0:0 r = 0.0, σ = 0., T = r = 0., σ = 0., T = r = 0.0, σ = 0.0, T = r = 0.0, σ = 0., T = TREE: Binomial call and put approximation with points on the lattice. Bjerksund-Stensland [0] (BJST): Two-step boundary call and put approximation.

5 EXHIBIT Approximated option values Parameters: American Put r = b - d S = TREE BJST OQNT b = r = 0.0, σ = 0., T = b = r = 0., σ = 0., T = b = r = 0.0, σ = 0.0, 0... T = b = r = 0.0, σ = 0., T = TREE: Binomial call and put approximation with points on the lattice. Bjerksund-Stensland [0] (BJST): Two-step boundary call and put approximation. Approximated option values. Strike K = 00 r = 0.0, σ = 0., T = b = r = 0.0, σ = 0.0, T = b = r = 0.0, σ = 0., T = b = r = 0.0, σ = 0., T = 00 No early exercise... b = TREE: Binomial call and put approximation with points on the lattice. Bjerksund-Stensland [0] (BJST): Two-step boundary call and put approximation.