Evaluating Options Price Sensitivities Options Pricing Presented by Patrick Ceresna, CMT CIM DMS Montréal Exchange Instructor
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How an Option s Price is Determined 3
How an Option s Price is Determined Options are priced based on probabilities. These probabilities are calculated using different pricing formulas. The most well known being the Black Scholes Pricing Model.
5 Variables in Options Pricing
Variables in Option Pricing Option pricing models consider the following variables: 1. Price 2. Strike 3. Time 4. Volatility 5. Dividend 6. Interest
Price Option pricing models consider the following variables: 1. Price 2. Strike 3. Time 4. Volatility 5. Dividend 6. Interest The simplest variable to understand is the price. As the price of the stock increases or decreases, the option will change in value.
Strike Option pricing models consider the following variables: 1. Price 2. Strike 3. Time 4. Volatility 5. Dividend 6. Interest The strike price is the price at which option is exercisable. The closer the stock is to the strike, the higher the option value.
Time Option pricing models consider the following variables: 1. Price 2. Strike 3. Time 4. Volatility 5. Dividend 6. Interest The more time until expiration, the more expensive is the option.
Volatility Option pricing models consider the following variables: 1. Price 2. Strike 3. Time 4. Volatility 5. Dividend 6. Interest The more volatile a stock is, the more expensive the premium will be to reflect the risk of a sudden rapid price change.
Dividends Option pricing models consider the following variables: 1. Price 2. Strike 3. Time 4. Volatility 5. Dividend 6. Interest All known dividends are discounted from the price of the option.
Interest Option pricing models consider the following variables: 1. Price 2. Strike 3. Time 4. Volatility 5. Dividend 6. Interest The risk free rate of interest is factored into the price of an option.
13 Option Greeks
Option Greeks The Greeks measure the change in value of an option due to a change in one of the pricing variables. Professional traders and market makers use the Greeks to create hedged positions. Investors use them to understand how a change in one of the variables will influence the option price.
Variables in Options Pricing The Greeks: 1. Delta 2. Gamma 3. Vega 4. Theta 5. Rho
16 Delta
Delta (Change in Price) Delta is a mathematical measure used to show the change in an option price relative to a change in the price of the underlying security.
Delta A delta of 0.900 Option price will increase $0.90 for every $1.00 in the increase in the stock. A delta of 0.450 Option price will increase $0.45 for every $1.00 in the increase in the stock.
Delta Example Stock price: $50.00 Option strike: $50.00 Time: 30 days Call option price: $2.32 Delta: 0.530 Stock price: $51.00 Option strike: $50.00 Option price: $2.85 *Assuming all other variables stay the same Stock price: $49.00 Option strike: $50.00 Option price: $1.79
Delta Stock vs. Option XIU trading at $20.00 a share XIU 1mth $20.00 call at a delta of 0.50 Position Notional Position Size Delta Exposure 1000 shares $20,000 $20,000 10 x 1/mth $20 calls $20,000 $10,000 20 x 1/mth $20 calls $40,000 $20,000
Delta As a call option becomes deeper in-the-money, the delta will approach 1. Call options always have a positive delta. As a put option becomes deeper in-the-money, the delta will approach -1. Put options always have a negative delta.
Delta on Calls ishares S&P/TSX60 ETF (XIU) $21.45 (September 1, 2016) 0.00 0.50 1.00
Delta on Puts ishares S&P/TSX60 ETF (XIU) $21.45 (September 1, 2016) -1.00-0.50 0.00
24 Delta and Probabilities
Implied Volatility Variable Implied Volatility is the probability adjustment within the option pricing model. It creates a probabilities distribution curve.
Understanding the Anticipated Range ABC stock is trading at $50.00. The implied volatility is 10%. 10% of $50.00 is $5.00.
Implied Volatility and Probability Range ABC stock at $50.00 with 10% Implied Volatility $45 68.2% $55 $35 $40 $45 $50 $55 $60 $65
Call Options Chain Plot Time Value
The Probability Distribution 50% Probabilities 50% Probabilities Lower Higher 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 Start Price
1 Standard Deviation 16% Probability 68% Range 16% Probability 27 21 22 23 24 25 26 28 29 30 31 32 34 35 36 37 38 39 33
Probabilities of an OTM Call Stock at $30.00 Long $34.00 call option 84% Probability of Expiring 16% Probability 21 22 23 24 25 26 27 28 29 31 32 33 35 36 37 38 39 30 34
Delta and Probabilities Many traders observe delta as an approximation of the probabilities of ending in the money. Delta of 0.90 is pricing a 90% of exercise. Delta of 0.50 is pricing a 50% of exercise. Delta of 0.10 is pricing a 10% of exercise.
Delta and Probabilities ishares S&P/TSX60 ETF (XIU) $21.45 (September 1, 2016) 21.50
Delta and Probabilities ishares S&P/TSX60 ETF (XIU) $21.45 (September 1, 2016) 20.00
Delta and Probabilities ishares S&P/TSX60 ETF (XIU) $21.45 (September 1, 2016) 22.50
36 Gamma
Gamma (Change in Delta) Gamma is the rate of change in the delta. It is the second derivative (delta of the delta).
Gamma (Change in Delta) Simple relationship the shorter the time till expiration, the higher the gamma sensitivity. It plays an important factor for professional traders who are using options to delta hedge their portfolios and market makers trying to achieve a delta neutral exposure.
Gamma (Change in Delta) ishares S&P/TSX60 ETF (XIU) $21.45 (September 1, 2016) Gamma
Gamma and Duration ishares S&P/TSX60 ETF (XIU) $21.45 (September 1, 2016) Gamma
Gamma and Position Delta Exposure XIU trading at $20.00 a share XIU 1 month $20.00 call at a delta of 0.521 XIU 6 month $20.00 call at a delta of 0.541 Position Notional Position Size Position Delta exposure $20.00 Position Delta exposure at $21.00 Position Delta exposure at $22.00 1000 shares $20,000 $20,000 $20,000 $20,000 Gamma Higher on 1mth 10 x 1/mth $20 calls $20,000 $10,420 $16,452 $19,218 10 x 6/mth $20 calls $20,000 $10,820 $14,140 $16,670 Gamma Lower on 6mth
42 Vega
Vega (Volatility) Vega is a measure of change in an option price relative to a 1 percent change in implied volatility. Vega is not bound to the 0 to 1 range like other Greeks. Vega will always be higher on higher priced options.
Expanding Implied Volatility The environment changes anticipating a period of high volatility. The volatility will expand adjusting the price of options. The rate of change measure called the Vega.
Expanding Implied Volatility 68% Range Original SD Range 21 22 23 24 25 28 29 30 26 27 32 33 34 31 35 36 37 38 39
Contracting Implied Volatility The environment changes anticipating a period of less volatility. The volatility will contract adjusting the price of options. Rate of change measure called the Vega.
Contracting Implied Volatility 68% Range Original SD Range 26 29 30 27 28 32 33 21 22 23 24 25 31 34 35 36 37 38 39
Vega Example Stock Price: $50.00 (remains unchanged) Strike Price: $50.00 Time: 30 days Option Price: $2.06 Implied Volatility: 35% Vega: 0.057 Implied Volatility: 36% Vega: 0.057 Option Price: $2.12 *Assuming all other variables stay the same Implied Volatility: 34% Vega: 0.057 Option Price: $2.00
Vega (Volatility) Vega only influences time value (not intrinsic value). Therefore at-the-money options will have the largest Vega influence.
Vega XIU trading at $21.50 a share (September 1, 2016) Vega
51 Theta
Theta (Time) Theta is the measure of change in an option price relative to a change in the time until expiration. Every day that passes, an option loses time value. Theta measures the rate of that time decay.
Theta Example Stock price : $50.00 (remains unchanged) Strike price: $50.00 Option price: $2.06 Time: 30 Days Theta: -0.041 Time: 29 Days Theta: -0.041 Option price: 2.02 *Assuming all other variables stay the same
Theta (Time) Theta only influences time value (not intrinsic value). Therefore Theta is highest at-the-money.
Theta XIU trading at $21.50 a share Theta
Time Decay and Weekends Time does decay over weekends. If this was not discounted into the price, it would create an easy way for traders to profit. Market makers generally do not want to get stuck with theta losses over the weekend. Therefore options often are discounted to move inventory.
57 Rho
Rho (Interest Rates) Rho is the measure of change in an option price relative to a change in the risk-free rate of interest.
Rho Example Stock price: $50.00 (remains unchanged) Strike price: $50.00 Time: 30 days Option price: $2.06 Interest Rates: 3.00% Rho: 0.020 Interest Rates: 4.00% Rho: 0.020 Option Price: $2.08 *Assuming all other variables stay the same Interest Rates: 2.00% Rho: 0.020 Option Price: $2.04
Rho and ZIRP/NIRP Zero bound (or negative bound) interest rates marginalize the influence in options pricing. It is likely Rho would once again play a significant role in a period of inflation.
Summary By learning the options Greeks, an investor will: Understand why an option is or is not moving in correlation with the underlying stock Construct strategies to offset the impact of certain pricing variables such as volatility and time depreciation Better manage performance expectations
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