A bank has just sold a call option on 500,000 shares of a stock. The strike price is 40; the stock price is 40; the risk-free rate is 5%; the volatility is 30%; and the time to maturity is 3 months. a. What position should the company take in the stock for delta neutrality? b. Suppose that the bank does set up a delta-neutral position as soon as the option has been sold and the stock price jumps to 42 within the first hour of trading. What trade is necessary to maintain delta neutrality? Explain whether the bank has gained or lost money in this situation.
Added by Jose Luis B.
Step 1
First, we need to calculate the delta of the call option. We can use the Black-Scholes formula for this. The formula for delta is: $$ \Delta = N(d_1) $$ where $N(d_1)$ is the cumulative normal distribution function of $d_1$, and $d_1$ is given by: $$ d_1 = Show more…
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