Options II

Options II - Econ 174 FINANCIAL RISK MANAGEMENT LECTURE...

Info iconThis preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon
Econ 174 – FINANCIAL RISK MANAGEMENT LECTURE NOTES Foster, UCSD October 16, 2011 OPTIONS II – OPTION PRICING THEORY A. Simple Patterns in Option Prices 1. Preliminaries and Notation: a) The value of an option at time t is the premium C t or P t at which it can be bought or sold. b) Because option holders can’t be forced to exercise at a loss, C t and P t are never negative: Both C and P ≥ $0 c) The premium value has two components. 1) Intrinsic value (“exercise value”) = max {immediate payoff, 0}. Intrinsic value of call S t - K > 0 or 0 Intrinsic value of put K - S t > 0 or 0 2) Time value (“speculative value”) = total value (P t or C t ) − intrinsic value. d) Examples. [Table 1] 1) July $21 call with C t = $1.68. Immediate payoff = S t - K = $21.24 - $21 = $0.24 > 0, so this option is in the money intrinsic value = $0.24; time value = C t - $0.24 = $1.44 2) April $19 put with P t = $0.50. immediate payoff = K - S t = $19 - 21.24 < $0, so this option is out of the money intrinsic value = $0; time value = P t - $0 = $0.50 3) Note that, ceteris paribus : Both P and C are higher for options with longer-term T. For example, the $23 puts all have the same intrinsic value K – S 0 = 23 - 21.24 = $1.76, so the greater time value must be due to the longer-term. C is lower and P is higher for options with bigger K. 2. Principles of Portfolio Replication: Stock Option Notation (for 0 t T) t = 0…τ… T Now, early exercise date, expiration date T-t Time remaining to maturity at time t (yrs) S t Spot (stock market) price of stock ($/share) K Strike (exercise) price ($/share) C, P American put/call option premium ($/share) c, p European put/call option premium ($/share) C t (T), etc. Premium at time t of option expiring at T D PV of known dividends (discount at r f ) Table 1. INTEL STOCK OPTIONS (Jan 14, 2010) S 0 = $21.24 Calls Puts K FE B APR JUL FEB APR JUL $19 $21 $23 $2.3 1 0.90 0.21 $2.5 7 1.28 0.49 $2.9 6 1.68 0.82 $0.1 8 0.81 2.15 $0.5 0 1.20 2.85 $0.9 2 1.66 2.90
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Ec 174 OPTIONS II p. 2 of 17 a) These variations on the “Law of One Price” are used heavily in the arbitrage arguments underlying most option pricing theory. b) Consider portfolios A and B and future states of the world i = 1…m: Portfolio A costs A 0 to obtain today and will be worth {A(i) T , i = 1…m} at time T Portfolio B costs B 0 to obtain today and will be worth {B(i) T , i = 1…m} at time T c) From these, we can deduce the following principles: #1 If the distribution of values {A(i) T } {B(i) T }, then the current values A 0 = B 0 , or else an arbitrage opportunity exists. #2 If all values in the distribution in {A(i) T } ≥ values in the distribution in {B(i) T }, then A 0 B 0 , or else an arbitrage opportunity exists. #3
Background image of page 2
Image of page 3
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 10/16/2011 for the course ECON 174 taught by Professor Foster,c during the Fall '08 term at UCSD.

Page1 / 17

Options II - Econ 174 FINANCIAL RISK MANAGEMENT LECTURE...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online