The current time is t = 0 (in years). Assume the Black-Scholes framework. You are given:

(i) The current stock price is 40.

(ii) The stock’s volatility is 40%.

(iii) The stock pays dividends continuously at a rate proportional to its price. The dividend yield is 2%.

(iv) The continuously compounded risk-free interest rate is 8%.

A market-maker has just sold 100 chooser options (also known as as-you-like-it options) on the above stock. At t = 0.25, the holder of each chooser option will choose whether it becomes a European call option or a European put option, each of which will expire at t = 1 with a strike price of $42. The market-maker delta-hedges his/her position with shares of the stock.

Calculate the initial number of shares in the market-maker’s delta-hedging program.