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![]() risk free and risky assets and the market price of risk | ![]() European calls and puts, a straddle and a butterfly spread | ![]() Itos lemma, Black-Scholes equation and a perpetual option | ![]() forward contract, Black-Scholes equation and an option on a future | ![]() Black-Scholes equation, a European down-and-out call and the payoff of a portfolio |