restrictionsonoptionsprices(衍生金融工具-人民-免費閱讀
【正文】 ., for T2 T1, C(S,K,t,T2)?C(S,K,t,T1) P(S,K,t,T2)?P(S,K,t,T1) Note: This does not always hold for European options. (Why?) F. An American option is worth at least its exercise value (what you would get if you exercise today). C(S,K,t,T)?max[0,S(t)K] P(S,K,t,T)?max[0,KS(t)] Example: Do we have an arbitrage opportunity if, for Intel stock with S(t) = $100, a call option with K=$90 and 6month to maturity is trading at $9? Note: This rule does not always hold for European options. (Why?) ? More Arbitrage Bounds for Options on NonDividendPaying Stocks: Example: Same as on the previous page. Assume S(t)=$100, and the price of an Intel call with K=$90 and 6month to maturity is $11. Assume that Intel will not pay any dividend within the next 6month and assume that the risk free interest rate (.) is 10%. Is there an arbitrage? A. For a stock does not pay dividends: c(S,K,t,T)?max[0,S(t)KB(t,T)] C(S,K,t,T)?max[0,S(t)KB(t,T)] Proof: To prove this we only need to show (why?) c(S,K,t,T)?S(t)KB(t,T) We show this by contradiction. If c SKB, we have an arbitrage. This implies that American calls on nondividendpaying stocks will never be exercised earlier. (Intuition?) An arbitrage: Transaction Payoff (at t) Payoff (at T) c St KB Max[0,S(T)K] S(T) K SKBc Max[0,S(T)K] [S(T)K] B. For European puts on nondividendpaying stocks, a similar arbitrage argument shows that: Intuition?) p(S,K,t,T)?max[0,KB(t,T)S] C. Combining these rules implies that the value of a European call on a nondividendpaying stock must lie in the region: max[0,S(t)KB(t,T)]?c(S,K,t,T)?S(t). 0 KB(t,T) S(t) D. Combining the rules for European puts, we see that the value of a European put on a nondividendpaying stock must lie in the region: max[0,KB(t,T)S(t)]?p(S,K,t,T)?KB(t,T) KB(t,T) S(t) E. Is it possible to early exercise American Puts on nondividendpaying stocks? Intuitions? Example: S(t)=$1, K=$25, Tt=6month, r=% () ? PutCall Parity for Nondividendpaying stocks A. For E
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