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