Important Concepts Important Concepts Some important concepts in financial and derivative markets Lecture 2 2: Basic Principles of Option Pricing Lecture 2.2: Basic Principles of Option Pricing Concept of intrinsic value and time value Concept of time value decay Concept of time value decay Effect of volatility on an option price y p p Nattawut Nattawut Jenwittayaroje Jenwittayaroje, Ph.D., CFA , Ph.D., CFA Put-call parity 01135531: Risk Management 01135531 : Risk Management and Financial Instrument and Financial Instrument d Fi d Fi i l I i l I t t t t Chulalongkorn University Chulalongkorn h l l h l l k k University nattawut@cbs.chula.ac.th nattawut@cbs.chula.ac.th 2 1 Some Important Concepts in Financial and Some Important Concepts in Financial and Derivative Markets Derivative Markets Risk Preference Ri k P f Arbitrage and the Law of One Price Risk aversion vs. risk neutrality Law of one price: same good must be priced at the same price Law of one price: same good must be priced at the same price Risk premium – an additional return a risk-averse investor expect Arbitrage defined: A type of profit-seeking transaction where the to earn on average to take a risk. same good trades at two prices buy one at low price and sell the same good trades at two prices buy one at low price and sell the Short Selling other with high price. Short selling on a stock is selling a stock borrowed from someone Example: See Figure 1.2 -> The concept of states of the world E l S Fi 1 2 > Th t f t t f th ld else (e.g., a broker). The Law of One Price requires that equivalent combinations of Short selling is done in the anticipation of the price falling, at assets, meaning those that offer the same outcomes, must sell for a which time the short seller would then buy back the stock at a single price or else there would be an opportunity for profitable lower price, capturing a profit and repaying the shares to the broker. arbitrage that would quickly eliminate the price differential. 3 4
Some Important Concepts in Financial and Basic Notation and Terminology Basic Notation and Terminology Derivative Markets Symbols S 0 = stock price today where time 0 = today S 0 stock price today, where time 0 today X = exercise price T = time to expiration in years = (days until expiration)/365 r = risk free rate S T = stock price at expiration C(S 0 T X) = price of a call option in which the stock price is S 0 the C(S 0 ,T,X) price of a call option in which the stock price is S 0 , the time to expiration is T, and the exercise is X P(S 0 ,T,X) = price of a put option in which the stock price is S 0 , the P(S T X) i f t ti i hi h th t k i i S th time to expiration is T, and the exercise is X 5 6 Basic Notation and Terminology Basic Notation and Terminology Principles of Call Option Pricing Principles of Call Option Pricing Concept of intrinsic value: C f i i i l Intrinsic value (IV) is the value the call holder receives from exercising the option. So IV is positive for in-the-money calls and zero for at- and out-of-the-money calls S 0 =$125, X=$120, then IV=5 S 0 =$120, X=$120, then IV=0 S 0 =$118, X=$120, then IV=0 7 8
Principles of Call Option Pricing Principles of Call Option Pricing Concept of time value f i l C The price of an American call normally exceeds its intrinsic value. The difference between the option price and the intrinsic value is called the time value or speculative value . The time value/speculative value reflects what traders are willing to pay for the uncertainty of the underlying stock. See Table 3.2 for intrinsic and time values of DCRB calls The time value is low when the call is either deep in- or deep-out-of- p p the-money. Time value is high when at-the-money…. The uncertainty (about the call expiring in- or out-of-the-money) The uncertainty (about the call expiring in or out of the money) is greater when the stock price is near the exercise price. 10 Principles of Call Option Pricing (continued) Principles of Call Option Pricing (continued) Principles of Call Option Pricing (continued) Principles of Call Option Pricing (continued) Concept of time value decay Effect of Stock Volatility The higher the volatility of the underlying stocks, the higher g y y g , g As expiration approaches (i.e., short time remaining for an s e p o pp o c es ( .e., s o e e g o the price of a call option), the call price loses its time value “time value Intuition…. Intuition…. decay”. decay . If the stock price increases, the gains on the call increase. At expiration, the call price curve collapses onto the intrinsic value time value goes to zero at expiration. ti If the stock price decreases, it does not matter since the If the stock price decreases it does not matter since the l l t t i ti potential loss on the call is limited. 11 12
Principles of Put Option Pricing Principles of Put Option Pricing Principles of Put Option Pricing Principles of Put Option Pricing Concept of intrinsic value: Concept of time value Intrinsic value (IV) is the value the put holder receives from ( ) p The price of an American put normally exceeds its intrinsic The price of an American put normally exceeds its intrinsic exercising the option. So IV is positive for in-the-money puts value. The difference between the option price and the intrinsic and zero for at- and out-of-the-money puts and zero for at and out of the money puts value is called the time value or speculative value value is called the time value or speculative value. S 0 =$125, X=$120, then IV=0 The time value/speculative value reflects what traders are willing S 0 =$120, X=$120, then IV=0 S $120 X $120 h IV 0 to pay for the uncertainty of the underlying stock. S 0 =$118, X=$120, then IV=2 See Table 3.7 for intrinsic and time values of DCRB puts. The time value is largest when the stock price is near the exercise price exercise price. 13 Principles of Put Option Pricing (continued) Principles of Put Option Pricing (continued) Concept of time value decay As expiration approaches (i e short time remaining for an As expiration approaches (i.e., short time remaining for an option), the put price loses its time value “time value decay” decay . At expiration, the put price curve collapses onto the intrinsic value time value goes to zero at expiration. 15 16
Principles of Put Option Pricing (continued) Principles of Put Option Pricing (continued) Put-Call Parity: European Options Put-Call Parity: European Options The prices of European puts and calls on the same stock with identical The Effect of Stock Volatility exercise prices and expiration dates have a special relationship. The effect of volatility on a put s price is the same as that for a The effect of volatility on a put’s price is the same as that for a Portfolio A: (1) Buying a put option with the same X as the call + (2) A call. Higher volatility increases the possible gains for a put holder. share. If the stock price decreases, the gains on the put increase. If the stock price decreases the gains on the put increase Cost of estiblishi ng the portfolio A : If the stock price increases, it does not matter since the P S where P , price of a put to sell one share 0 potential loss on the put is limited. 0 S current share price The higher the volatility of the underlying stocks, the higher the price of a put. At maturity, if S T > X , the put option is expired worthless, and the portfolio is worth S T . At maturity, if S T < X , the put option is exercised at option maturity, and the portfolio becomes worth X . 17 18 Put-Call Parity: European Options Put Call Parity: European Options Put-Call Parity: European Options Put-Call Parity: European Options Portfolio B: (1) Buying a call option + (2) buying risk-free zero-coupon T-bills with face value equal to the exercise price of the call (X) Cost of estiblishi ng the portfolio B : X C C where h C C , price i of f a call ll to t buy b one share h T r 1 the T-bills will worth X at the maturity. At maturity, if S T > X , the call option is exercised and portfolio A is A i if S X h ll i i i d d tf li A i worth S T . At maturity, if S T < X , the call option expires worthless and the portfolio is worth X . 19 20
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