Derive a formula for the volga of a European call option on a no-dividend underlying asset...

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Derive a formula for the volga of a European call option on ano-dividend underlying asset in the Black-Scholes model.

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The BlackScholes formula calculates the price of European putand call options This price is consistent with the BlackScholesequation as above this follows since the formula can be obtainedby solving the equation for the corresponding terminal and boundaryconditionsThe value of a call option for a nondividendpaying underlyingstock in terms of the BlackScholes parameters isThe price of a corresponding put option based on putcall parityisFor both as aboveis the cumulative distribution function of the standard normaldistributionis the time to maturity expressed in yearsis the spot price of the underlying assetis the strike priceis the riskfree rate annual rate expressed in terms ofcontinuous compoundingis the volatility of returns of the underlying assetAlternative formulationeditIntroducing some auxiliary variables allows the formula to besimplified and reformulated in a form that is often more convenientthis is a special case of the Black 76 formulaThe auxiliary variables areis the time to expiry remaining time backward timeis the discount factoris the forward price of the underlying asset and displaystyleSDFwith See Answer

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