Question

B. decreases by approximately 4.3%. C. decreases by approximately $1.72. Answer C The put option will decrease in value as the underlying stock price increases: -0.43 x S4 S1.72. 100,000 Stocks Call Option sold has the following details. The stock price is $49, the strike price is $50, the risk-free rate is 5%, the stock price volatility is 20%, and the time to exercise is 20 weeks or 20/52 year. Table below shows Delta, Gamma, Vega, Theta and Rho for the option (i.e., for a long position in one option) Single Option Value (S) Delta (per $) Gamma (per S) Vega (per %) Theta (per day) Rho (per 00) $2.40 0.522 0.121 -0.012 0.089 a. When there is an increase of S0.1 in the stock price with no other changes, calculate the change in the value of the 100,000 short option positions due to Delta. When there is an increase of $0.1 in the stock price with no other changes, calculate the change in the value of the 100,000 short option positions due to Gamma. b. when there is an increase in volatility of 0.5% from 20% to 20.5% with no other changes, calculate the change in the value of the 100,000 short option position due to Vega e, When one day goes by with no changes to the stock price or its volatility, calculate the change in the value of the 100,000 short option position due to Theta. d. when interest rates increase by 1% (or 100 basis points) with no other changes, calculate the change in the value of the 100,000 short option position due to Rho. e

Answer 1

Stock price	49
Strike price	50
Rf	5%
Volatility	20%
T	20/52
Position (# of stocks)	100000

Parameter	Change	Change in Underlying (Stock price, interest rate. volatility, time )	Change in 1 call option value	Change in position value (100,000)	Increase/ decrease
Delta (/$)	0.522	0.1	0.0522	5220	Decrease
Gamma (/$)	0.066	0.1	0.0066	660	Decrease
Vega (/%)	0.121	0.5	0.0605	6050	Decrease
Theta (/day)	-0.012	1	-0.012	1200	Increase
Rho (/%)	0.089	1	0.089	8900	Decrease