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t = 9 0 d a y ss = 3 0 %C a l l P r i c e = 3 . 2 7P u t P r i c e = 2 . 6 5C P S Xe rt? ? ? ?Synthetic Long Put Position ? We can create a synthetic long position in a put by buying a call, selling the stock, and lending the strike price at the riskfree rate until expiration 5 0 0 04 0 0 03 0 0 02 0 0 01 0 0 00100020223000400050000 20 40 60 80 100Sto c k Pr i c e a t Ex p i r a ti o nProfitS t o c k P r o f i t C a l l P r o f i t L e n d a t R i s k f r e e S t r a t e g y P r o f i tS = 5 0 X = 5 0r = 5 % t = 9 0 d a y ss = 3 0 %C a l l P r i c e = 3 . 2 7P u t P r i c e = 2 . 6 5P C S Xe rt? ? ? ?Synthetic Short Stock Position ? We can create a synthetic short position in the stock by selling a call, buying a put, and borrowing the strike price at the riskfree rate until expiration 5 0 0 04 0 0 03 0 0 02 0 0 01 0 0 00100020223000400050000 20 40 60 80 100Sto c k Pr i c e a t Ex p i r a ti o nProfitP u t P r o f i t C a l l P r o f i t B o r r o w a t R i s k f r e e S t r a t e g y P r o f i tS = 5 0 X = 5 0r = 5 % t = 9 0 d a y ss = 3 0 %C a l l P r i c e = 3 . 2 7P u t P r i c e = 2 . 6 5? ? ? ? ?S P C Xe rtSynthetic Short Call Position ? We can create a synthetic short position in a call by selling a put, selling the stock, and lending the strike price at the riskfree rate until expiration 5 0 0 04 0 0 03 0 0 02 0 0 01 0 0 00100020223000400050000 20 40 60 80 100Sto c k Pr i c e a t Ex p i r a ti o nProfitP u t P r o f i t S t o c k P r o f i t L e n d a t R i s k f r e e S t r a t e g y P r o f i tS = 5 0 X = 5 0r = 5 % t = 9 0 d a y ss = 3 0 %C a l l P r i c e = 3 . 2 7P u t P r i c e = 2 . 6 5? ? ? ? ? ?C P S Xe rtSynthetic Short Put Position ? We can create a synthetic short position in a put by selling a call, buying the stock, and borrowing the strike price at the riskfree rate until expiration 5 0 0 04 0 0 03 0 0 02 0 0 01 0 0 00100020223000400050000 20 40 60 80 100Sto c k Pr i c e a t Ex p i r a ti o nProfitS t o c k P r o f i t C a l l P r o f i t B o r r o w a t R i s k f r e e S t r a t e g y P r o f i tS = 5 0 X = 5 0r = 5 % t = 9 0 d a y ss = 3 0 %C a l l P r i c e = 3 . 2 7P u t P r i c e = 2 . 6 5? ? ? ? ?P S C Xe rtOption Valuation ? The value of an option is the present value of its intrinsic value at expiration. Unfortunately, there is no way to know this intrinsic value in advance. ? The most famous (and first successful) option pricing model, the BlackScholes OPM, was derived by eliminating all possibilities of arbitrage. ? Note that the BlackScholes models work only for Europeanstyle options. Option Valuation Variables ? There are five variables in the BlackScholes OPM (in order of importance): ? Price of underlying security ? Strike price ? Annual volatility (standard deviation) ? Time to expiration ? Riskfree interest rate Variables’ Affect on Option Prices Call Options ? Direct ? Inverse ? Direct ? Direct ? Direct Put Options ? Inverse ? Direct ? Direct ? Inverse ? Direct Variable – Stock Price – Strike Price – Volatility – Interest Rate – Time Option Valuation Variables: Underlyin