FRM Powerpoints 2011 Unit IID Option Contracting

# FRM Powerpoints 2011 Unit IID Option Contracting - II....

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II. Tools and Applications of Market Risk Management D. Option Contracting

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Version: January 3, 2011 Unit II.D p. 2 of 95 Characteristics of Options o An option is a contract between two parties in which one party, the buyer, has the right to buy or sell an asset or other derivative at a fixed price for a definite period of time. The buyer pays the other party, the seller or writer, the option price or premium. The right to buy is referred to as a call and the right to sell is referred to as a put. The fixed price is called the exercise price. If the option can be exercised at any time up to expiration, it is called an American option. If the option can be exercised only at expiration, it is called a European option. The buyer is said to be “long” the option and the seller is said to be “short.” o Exchange-listed and OTC options o Quotes at http://www.optionseducation.org/quotes/default.
Version: January 3, 2011 Unit II.D p. 3 of 95 Characteristics of Options (cont.) o Exchange-listed options volume in 2009 was 9.5 billion contracts o June 2010 BIS figures show n Currency options: \$11.2 trillion notional principal and \$411 billion market value n Interest rate options: \$48.1 trillion notional and \$1.5 trillion market value n Equity options: \$4.5 trillion notional and \$518 billion market value **This page updated annually

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Version: January 3, 2011 Unit II.D p. 4 of 95 Option Payoffs o Payoff = value at expiration o Notation n X = exercise price of the option n ST = price of the underlying asset at time T (expiration) n CT = value (price) of a call option at time T (expiration) n PT = value (price) of a put option at time T (expiration) n S0 = value of the underlying asset at time 0 (today) n C0 = value of call at time 0 (today) n P0 = value of put at time 0 (today)
Version: January 3, 2011 Unit II.D p. 5 of 95 Option Payoffs (cont.) o Values at expiration: n Call: CT = Max(0,ST - X) n Put: PT = Max(0,X – ST) o These are values at expiration, not prior to expiration

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Version: January 3, 2011 Unit II.D p. 6 of 95 Basic Principles of Option Valuation o Put-Call Parity Value of Instrument at Time 0 Value of Instrument at Time T ST ≤ X ST > X Combination A Long stock S0 ST ST Long put P0 X – ST 0 Total S0 + P0 X ST Combination B Long call C0 0 ST – X Long bond X(1 + r)-T X X Total C0 + X(1 + r)- T X ST
Version: January 3, 2011 Unit II.D p. 7 of 95 Basic Principles of Option Valuation (cont.) o Put-Call Parity (cont.) n C0 + X(1 + r)-T = P0 + S0 n Rearrangements of put-call parity o P0 = C0 - S0 + X(1 + r)-T o C0 = P0 + S0 - X(1 + r)-T o S0 = C0 - P0 + X(1 + r)-T o X(1 + r)-T = S0 - C0 + P0 o And more o Make sure you can derive each of these using arbitrage

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Version: January 3, 2011 Unit II.D p. 8 of 95 Basic Principles of Option Valuation (cont.) o Put-Call Parity (cont.) n Note that a forward contract replicates a long stock, short risk-free bond position o Let X be the forward price o S0 – X(1 + r)-T is the value of the forward contract o Then, C0 + X(1 + r)-T = P0 + F(1 + r)-T
Version: January 3, 2011 Unit II.D p. 9 of 95 Basic Principles of Option Valuation (cont.) o Limitations on the Value of Options n Result 1. The value of a call cannot be negative.

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## This note was uploaded on 02/28/2012 for the course FIN 7400 taught by Professor Donchance during the Fall '11 term at LSU.

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FRM Powerpoints 2011 Unit IID Option Contracting - II....

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