restrictionsonoptionsprices(衍生金融工具-人民(編輯修改稿)
2025-03-04 05:29 本頁(yè)面
【文章內(nèi)容簡(jiǎn)介】 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 European options: S(t)=c(S,K,t,T)p(S,K,t,T)+KB(t,T) Intuition: a certain portfolio of bonds and options has the same payoff at maturity as a share of stock, so it must have the same price as a share of stock. Example: K=50, S=50, r=0, Tt=1 month, c=, p= ? S?cp+KB What should you do if these were the true prices? Transaction Initial (t) Cashflow Final (T) Cashflow S(T) 50 S(T)50 $50 $ $ $50 S(T) 0 $50S(T) $50 S(T) [S(T)$50] 0 $50 $ 0 0 B. Static Replication with PutCall Parity We can make synthetic stock, call, put, and bond using the PutCall Parity. For European options on a nondividendpaying stock, we have: Synthetic stock: S=cp+PV(K) Synthetic call: c=S+pPV(K) Synthetic put: p=cS+PV(K) Synthetic bond: PV(K)=Sc+p Question: How is the PutCall Parity related to the value of a forward contract on a stock (whose delivery price is equal to the strike price K)? C. PutCall Parity for American O
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