A. Consider an at-the-money (ATM) short straddle position (i.e. a position obtained by selling an equal number of put and call options with the same strike price). a scenario in which underlying stock price remains unchanged and implied volatility drop substantially would result in a decrease in gamma

B. consider a contingent claim XT= f(T,(rt)t[0,T]) for some deterministic function f) where the process (rt)t0, as well as zero coupon bonds with maturities T1 and T2 are traded in the market ( with 0 < T1< T < T2 ). There are no transaction costs and unconstrained borrowing/ lending is available at the risk free rate. Risk-neutral valuation yields a unique price xt of XTat some time t [0,T]

C . you are a firm with a variable interest payment L( T, S) due at time s, where T< S denotes the rest date. At time 0, you enter a bilateral trade in an S - year receiver forward rate agreement (FRA) with forward rate K and reset date T < S for the variable payment of the floating rate L(T,S) . As a result of the trade, you turn your variable rate liability into a fixed rate one

D. consider a payer swap you entered into to lock in swap rate equal to K > 0. At time u (0,T), you mark to your market position based on swap rate quotes on swap contracts with residual maturity T -u and reset/payment fate coinciding with those payer swap already in your portfolio. The market quotes a (counterparty risk free) swap rate s(u) >K at the time u. Assuming your counterparty is credit risk free, your position is making money

E. consider the same position as in question c above. Your counterparty is credit risky, whereas you are not. The market value of your FRA decreases relative to the risk free case of question c above.