1. Suppose that the stock price today is S(t) = 1, the interest rate is zero, the volatility is o = 0.02 and the time to maturity is three months. Consider a claim whose Black-Scholes price is given by the function C(t, s) = se (T-t), where time is in annual terms. (a) If your portfolio is long 10 of these claims and holds N shares of the stock, what should the value of N be so that the portfolio is delta-neutral? Use the minus sign for shorting. (b) Suppose that another claim with the same maturity is available with the Black-Scholes price given by the function c(t, s) = se0(T-t). If you still hold 10 units of the first claim, how many shares of the stock and how many claims of the second type would you hold to create a portfolio that is both delta neutral and vega-neutral (vega equal to zero)? Use the minus sign for short positions. 1. Suppose that the stock price today is S(t) = 1, the interest rate is zero, the volatility is o = 0.02 and the time to maturity is three months. Consider a claim whose Black-Scholes price is given by the function C(t, s) = se (T-t), where time is in annual terms. (a) If your portfolio is long 10 of these claims and holds N shares of the stock, what should the value of N be so that the portfolio is delta-neutral? Use the minus sign for shorting. (b) Suppose that another claim with the same maturity is available with the Black-Scholes price given by the function c(t, s) = se0(T-t). If you still hold 10 units of the first claim, how many shares of the stock and how many claims of the second type would you hold to create a portfolio that is both delta neutral and vega-neutral (vega equal to zero)? Use the minus sign for short positions