August 25th, 2001, 2:46 pm
I don’t know any tricks fore such options, so why not just develop a sexy approximation for atm-atm compound options. That is where the underlying option is at-the-money forward, and also the option on the option is at-the-money. For call-on-call and put-on-call S*0.4*v*Sqrt(t)*(0.5+0.2*v*Sqrt(T))Where S is the asset price, v is the volatility, t is time to maturity compound option, T is time to maturity on underlying option. Take a close look! The first part is simply the value of a plain vanilla option with time to maturity tS*0.4*v*Sqrt(t) The second part is the delta of a call option with time to maturity T 0.5+0.2*v*Sqrt(T)For a call-on-put and put-on-put we get plain vanilla option with time to maturity t multiplied by the delta of a put option with time to maturity TS*0.4*v*Sqrt(t)*(0.5-0.2*v*Sqrt(T))How accurate:Assume S=70 (Futures), v=0.2, t=0.5, T=1.0, risk free rate 0.1Underlying option Strike=70, Underlying option value = 5.5759Option on option strike=5.5759Using the Geske formula (involving cumulative bivariate distribution) I get 2.1022Using my approximation I get 2.1383 You can find more info and VBA code for the Geske formula in my book: "The Complete God to Option Pricing Formulas. "Sorry, God should be Guide I think...Regards,EGH (The Collector)