The current price of Draftkings Stock (Ticker: DKNG) is $48.35/share. Suppose the risk-free rate is currently 2.4%...

The current price of Draftkings Stock (Ticker: DKNG) is $48.35/share. Suppose the risk-free rate is currently 2.4% (continuously-compounded) at all maturities. DKNG does not pay a dividend and there is no expectation that it will any time over the coming year. Consider a 7-month forward contract on DKNG (expiring in April).

What is the forward price that would preclude arbitrage on such a forward contract?
If the 7-month forward price on DKNG was $48.50, is there an arbitrage opportunity? If so, how would you exploit it?
Suppose you had a long position in a forward contract on DKNG with F = $48.50/share (expiring in April), and by the time you get to March (one month remaining on the contract), DKNG’s price has risen to $49.93. What is the value of your long contract? What would be the value of an analogous short contract?
Now consider call and put options on DKNG expiring in April with strikes of K=50 (K_put = K_call = 50). What is the largest lower bound on price of a call option on DKNG with K=50 and T=April? What about the comparable put option?

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jeff jeffy answered 2 years ago

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