Question

Problem 7 Using the information in the table below, derive your best estimate of the price of the put option, if at the same time the index level increases from 250 to 255, and the volatility increases from 10% to 14%. Assume that the changes happen instantaneously after the computation of the price and sensitivities given in the table below (no time decay). Underlying Type: Index Index Level: Volatility (% per year): Risk-Free Rate (% per year): Dividend Yield (% per yer) 250.00 10.00% 2.00% 1.00% Option Type: Bbck-Scholes - European imply Volatility Life (Years) Strike Price: 0.5000 250.00 Put O Cal Calculate Results: Price: 6.3953881 Delta (per $): -0.4554818 Gamma (per $ per $): 0.0223291 Vega (per %) 0.6977835 Theta (per day) -0.0156472 Rho (per %) 0.6013292 . MacBook Air

Answer 1

In order to calculate the Put Option price with given conditions, any of the online calculators can be used. When the given details are flowed into the calculator, it gives the option price.

Option Calculator Implied Volatility Strategies Custom Matrix About Underlying Price 255 Call Option Put Option Exercise Price 250 Theoretical Price 13.3103 7.0945 Delta 0.6179 -0.3821 Days Until Expiration 182.5 Gamma 0.0151 0.0151 Interest Rates Vega 0.6877 0.6877 Dividend Yield Theta -0.0342 -0.0207 Volatility 14 Rho 0.7174 -0.5202

As shown in above snapshot of the calculator, with no time decay, the Put Option price will be $7.0945, if index level (Underlying price) is 255 and the volatility is increased to 14%.