Question

You are an Equity Options trader at Morgan Stanley. You are approached by a client who wants to buy a security that has the following features: As long as General motors's share price never trades at or above $50 per share, the client receives nothing. However, if General motor's share price ever gets to trade at or above $50 per share, the client will receive at that time, from Morgan Stanley, a payment in cash equal to $10,000,000, after which the security expires. The contract is perpetual (it means it has no fixed end date and the security continues forever until it expires (i.e., until the price level of $50 per share is reached)).
General Motors can potentially go bankrupt in which case its shares become worthless (and assume that the shares would remain worthless forever). Assume that, in the absence of bankruptcy, the shares of General Motors will trade forever (no takeovers or delistings, for example).

The share price of General Motors today is $40 per share. Assume that General Motors will never pay a dividend and will never do share buybacks. Assume that the risk-free interest-rate is zero per cent and will be zero per cent forever. Assume that Morgan Stanley can never go bankrupt and also assume that Morgan Stanley continues to exist for ever (so it can never renege on this contract).

a) The client wants to buy the above-mentioned security today. What price (in dollars) do you quote? How do you hedge this security so that Morgan Stanley has no risk? Explain your strategy.
Assume the absence of arbitrage throughout. Assume that there are no transactions costs. Assume that you can freely trade General Motors shares and borrow or lend at the risk-free interest-rate.   

b) How would your answer in part (a) change if, instead of assuming that the risk-free interest-rate is zero per cent forever, the risk-free today is 3.85% per annum (continuously compounded) but will fluctuate through time as the Fed changes its monetary policy?

Answer 1

You are an Equity Options trader at Morgan Stanley. You are approached by a client who wants to buy a security that has the following features: