Obtaining a general exact formula for the values of these options is one of finance’s major unsolved problems. For 10 points each:
[10h] Name these options which give the holder the right, but not the obligation, to buy or sell an asset for a fixed price. Unlike a similarly named style of option, these derivatives may be executed at any time up to expiry.
ANSWER: American options (The other option style is European.)
[10m] In the special case of American calls, the optimal policy is just to buy at expiry, so they can be priced exactly using this doubly-eponymous model, under which a stock price evolves as a geometric Brownian motion.
ANSWER: Black-Scholes model [or Black-Scholes-Merton model]
[10e] The reason for waiting until expiry to execute a call is that buying at a fixed price becomes cheaper over time in real terms, since this quantity is positive. This quantity is the rate at which a bank pays out on a deposit.
ANSWER: interest rate