Question

Opion Raitr Call Option sold has the following details. The stock price is $49, the 100,000 Stocks the nsk-free rate is 5%, the stock price volatility is 20%, and the time 20 weeks or 20/52 year. Table below shows Delta, Gamma, Vega, Theta, position in one option) to and Rho for the option (i e, for a long Single Option Value (S) Delta (per $) Gamma (per S) Vega (per %) Theta (per day) Rho (per %) $2.40 0.522 0.066 0.121 -0.012 0.089 When there is an increase of SO. I 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 in volatility of O 5% from 20% to 205% with no other changes, calculate the change in the value of the 100,000 short option position due to Vega b c. 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 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. d, Suppose a stoc is currently trading at 100. An at-the-money call with a maturity of three months has the following price and greeks C5.598 Δ 0.565 0.032 e12.385 19.685 P 12.71 e stock price moves to S -101, what isthe predicted new option price (using the delta alone)? If the

Answer 1

Stock price Strike price Rf Volatility 49 50 5% 20% 20/52 Position (# of stocks) | 100000 Change In Underlylng (Stock price, Interest rate. volatilty, Change In 1 call optlon value Change ln (100,00o) 5220 660 6050 posltlon value Increase/ Change tlme) 0.522 0.066 0.121 Parameter decrease Decrease Decrease Decrease Increase Decrease Delta (/S) Gamma (/s) Vega (/%) Theta (/day) Rho (/96) 0.1 0.1 0.5 0.0522 0.0066 0.0605 0.012 0.089 0.012 1200 Activ Go to P 0.089 8900