To check the martingale property we need to show that

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: previous section we begin with the One period case There are two possible outcomes for the stock called heads (H ) and tails (T ). ⇠⇠ S1 (H ) = S0 u ⇠⇠ ⇠⇠ S 0 XX XX XX S1 (T ) = S0 d We assume that there is an interest rate r, which means that $1 at time 0 is the same as $(1 + r) at time 1. For the model to be sensible, we need 0 < d < 1 + r < u. (6.1) Consider now an option that pays o↵ V1 (H ) or V1 (T ) at time 1. This could be a call option (S1 K )+ , a put (K S1 )+ , or something more exotic, so we will consider the general case. To find the “no arbitrage price” of this option we suppose we have V0 in cash and 0 shares of the stock at time 0, and want to pick these to match the option price exactly: ✓ ◆ 1 1 V0 + 0 S1 (H ) S0 = V1 (H ) (6.2) 1+r 1+r ✓ ◆ 1 1 V0 + 0 S1 (T ) S0 = V1 (T ) (6.3) 1+r 1+r Notice that here we have to discount money at time 1 (i.e., divide it by 1 + r) to make it comparable to dollars at time 0. To find the values of V0 and 0 we define t...
View Full Document

This document was uploaded on 03/06/2014 for the course MATH 4740 at Cornell.

Ask a homework question - tutors are online