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Case I:
一開頭(t=0) payoff必然>0 然後到maturity (t=T) payoff必然>= 0
Case II:
一開頭(t=0) payoff必然=0 然後到maturity (t=T) payoff必然>0
1.) Market consists of at least one stock and one risk-less asset (i.e. money market, cash, or bond)
2.) The rate of return on the risk-less asset is constant and thus called the risk-free interest rate
3.) Stock price follows Geometric Brownian motion with constant μ and σ
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4.) The stock does not pay a dividend (We can generalize it later)
5.) There is no arbitrage opportunity in the market
6.) It is possible to borrow and lend any amount, even fractional, of cash at the risk-less rate
7.) It is possible to buy and sell any amount, even fractional, of the stock (this includes short selling)
8.) No transaction cost (i.e. friction-less market) (We can generalize it later)