Consider a 1-year European call option on a stock when the stock price is $30, the strike price is $30, the risk-free rate is 5%, and the volatility is 25% per annum. Compute the price, delta, gamma, vega, theta, and rho of the option under the Black-Scholes-Merton model. i Verify that delta is correct by changing the stock price to $30.1 and recomputing the option price. ii Verify that gamma is correct by recomputing the delta for the situation where the stock price is $30.1 iii) Carry out similar computations to verify that vega, theta, and rho are correct. Produce plots of the option price, delta, gamma, vega, theta and rho against the stock price for the stock option Consider a 1-year European call option on a stock when the stock price is $30, the strike price is $30, the risk-free rate is 5%, and the volatility is 25% per annum. Compute the price, delta, gamma, vega, theta, and rho of the option under the Black-Scholes-Merton model. i Verify that delta is correct by changing the stock price to $30.1 and recomputing the option price. ii Verify that gamma is correct by recomputing the delta for the situation where the stock price is $30.1 iii) Carry out similar computations to verify that vega, theta, and rho are correct. Produce plots of the option price, delta, gamma, vega, theta and rho against the stock price for the stock option