You just sold an at-the-money, European call option on a stock that is trading for $75 on the NYSE to one of your institutional clients. Similar options are trading at an implied volatility of 60% in the over-the-counter (OTC) market. The stock's dividend yield and the risk-free interest rate are equal to 2.5% and 3.5% per year, respectively. Both rates are continuously compounded. The contract is for 100,000 shares and it will expire in 365 days. (A) Using the Black-Scholes-Merton (BSM) formula, calculate the option contract's price along with its delta, gamma, vega, theta, and rho. How many shares of stock do you need to trade immediately to delta neutralize your position?

Answer rating: 100% (QA)

1 Calculate d1 and d2 d1 lnS K r q 2 2 T sqrtT d2 d1 sqrtT Plugging in the values d1 ln75 75 003... View the full answer