6 Options II

# 1012 2103 o if st 21 k 20 put expires exercise

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

This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: ⇒ p ≥ max {Ke−rT − (S0 – D0), 0} 3. Additional Arbitrage Opportunities when Bounds are Violated: a) Assume the following: rf = 10%/yr, T = 6 months, and S0 = \$25, D0 = 0 (no dividends). b) Example #1 – American or European call premium too high. 1) The upper bound is c ≤ C ≤ S0. Suppose that c = \$26 and S0 = \$25, so c > S0. 2) Arbitrage – write/sell call option for \$26, pay \$25 to buy the stock to cover it, and invest the \$1 at rf = 10%. By time T, you have cash worth (\$1)e0.10(1/2) = \$1.05, plus: • stock worth ST if option never exercised by holder; • cash worth at least K if option exercised and you sell stock to holder for K. 3) Either way, you make π > 0; arbs rushing to write (supply) this call and buy (demand) the stock will drive c down and S0 up until c ≤ S0. c) Example #2 – American put premium too high. 1) The upper bound is P ≤ K. Suppose that P = \$36 and K = \$35, so P > K. 2) Arbitrage – write/sell the put option for \$36 and invest it at rf = 10%. • If holder exercises at time τ, you buy his stock for \$35 and end with 36e0.10τ − 35 in cash plus stock worth Sτ; • If the holder never exercises, you end up with 36e0.10(1/2) = \$37.85. 3) Either way, you make π > 0; arbs rushing to write this call will drive P down until P ≤ K. Ec 174 OPTIONS II p. 7 of 18 d) Example #3 – European call premium too low. 1) The lower bound is c ≥ max {S0 − Ke−rT, 0}. Suppose that S0 = \$25, K = \$15, and c = \$9. Then c < 25 − 15e−0.10(1/2) = \$10.73. 2) Arbitrage opportunity. • At time t = 0, short- sell the stock to raise \$25 in cash, buy the call for \$9, and invest the remainder, S0 − c = \$16, at rf = 10%. • At time t = T: o If ST = \$20 > K = \$15, exercise the option, pay \$15 to buy stock and close out short position, and pocket (S0−c)erT − K = 16.82 − 15 = \$1.82/share. o If ST = \$10 < K = \$15, option expires. P...
View Full Document

## This document was uploaded on 02/18/2014 for the course ECON 174 at UCSD.

Ask a homework question - tutors are online