Starting at the right edge s3 ht t 2 but the maximum

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: er to sell this for $6.50. You are delighted when a customer purchases 10,000 calls for $65,000, but then become worried about the fact that if the stock goes up you will lose $85,000. By (6.7) the hedge ratio 15 = 1/2 0= 30 so you borrow $300,000 - $65,000 = $235,000 and buy 5,000 shares of stock. Case 1. The stock goes up to $80. Your stock is worth $400,000. You have to pay $150,000 for the calls and (19/18)$235,000 = $248,055 to redeem the loan so you make $1,945 (in time 1 dollars). Case 2. The stock drops to $50. Your stock is worth $250,000. You owe nothing for the calls but have to pay $248,055 to redeem the loan so again you make $1,945. The equality of the profits in the two cases may look like a miracle but it is not. By buying the correct amount of stock you replicated the option. This means you made a sure profit of the $1,842 di↵erence (in time 0 dollars) between the selling price and fair price of the option, which translates into $1,945 time 1 dollars. N period model To solve the problem in general we work backwards from the end, repeatedly applying 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