options

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Power options can lead to very high leverage and thus entail potentially very large losses for short positions in these options. It is therefore common to cap the payoff. The maximum payoff is set to some predefined level C. The payoff at maturity for a capped power call is min . Esser (2003) gives the closed-form solution: (via "The Complete Guide to Option...

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Standard power options (aka asymmetric power options) have nonlinear payoff at maturity. For a call, the payoff is max(S^i - X, 0), and for a put, it is max(X - S^i , 0), where i is some power (i > 0). The value of this power call is given by (see Heynen and Kat, 1996c; Zhang, 1998; and Esser, 2003). (via "The Complete Guide to Option Pricing Formulas") c = S^i...

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There are two main categories of power options. Standard power options' payoff depends on the price of the underlying asset raised to some power. For powered options, the "standard" payoff (stock price in excess of the exercise price) is raised to some power. A power contract is a simple derivative instrument paying (S/ X)^i at maturity, where i is some fixed...

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A moneyness option is basically a plain vanilla option where the strike is set to a percentage of the future/forward price. For example, a 120% moneyness call would have a strike equal to 120% of the forward price. A 120% moneyness put would have a spot equal to 120% of the strike. The value of this option is given in percent of the forward. The value of a...

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A forward start option with time to maturity T starts at-the-money or proportionally in- or out-of-the-money after a known elapsed time t in the future. The strike is set equal to a positive constant a times the asset price S after the known time t. If a is less than unity, the call (put) will start 1 - a percent in-the-money (out-of-the- money); if a is unity,...

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The Jennergren and Naslund (1993) formula takes into account that an employee or executive often loses her options if she has to leave the company before the option's expiration: (via "The Complete Guide to Option Pricing Formulas") c = e^(-lambda*T) * (Se^((b-r)T) * N(d1) - Xe^-rT * N(d2)) p = e^(-lambda*T) * (Xe^(-rT) * N(-d2) - Se^(b-r)T * N(-d1)) where ...

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Handley (2001) describes how to value variable purchase options (VPO). A VPO is basically a call option, but where the number of underlying shares is stochastic rather than fixed, or more precisely, a deterministic function of the asset price. The strike price of a VPO is typically a fixed discount to the underlying share price at maturity. The payoff at maturity...

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Perpetual American Options is Perpetual American Options pricing model. This indicator also includes numerical greeks. American Perpetual Options While there in general is no closed-form solution for American options (except for non-dividend-paying stock call options) it is possible to find a closed-form solution for options with an infinite time to...

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American Approximation Bjerksund & Stensland 2002 is an American Options pricing model. This indicator also includes numerical greeks. You can compare the output of the American Approximation to the Black-Scholes-Merton value on the output of the options panel. The Bjerksund & Stensland (2002) Approximation The Bjerksund and Stensland (2002) approximation...

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American Approximation Bjerksund & Stensland 1993 is an American Options pricing model. This indicator also includes numerical greeks. You can compare the output of the American Approximation to the Black-Scholes-Merton value on the output of the options panel. The Bjerksund and Stensland (1993) approximation can be used to price American options on stocks,...

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American Approximation: Barone-Adesi and Whaley is an American Options pricing model. This indicator also includes numerical greeks. You can compare the output of the American Approximation to the Black-Scholes-Merton value on the output of the options panel. An American option can be exercised at any time up to its expiration date. This added freedom...

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Samuelson 1965 Option Pricing Formula is an options pricing formula that pre-dates Black-Scholes-Merton. This version includes Analytical Greeks. Samuelson (1965; see also Smith, 1976) assumed the asset price follows a geometric Brownian motion with positive drift, p. In this way he allowed for positive interest rates and a risk premium. c = SN(d1) * e^((rho...

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Boness 1964 Option Pricing Formula is an options pricing model that pre-dates Black-Scholes-Merton. This model includes Analytical Greeks. Boness (1964) assumed a lognormal asset price. Boness derives the following value for a call option: c = SN(d1) - Xe^(rho * T)N(d2) d1 = (log(S / X) + (rho + v^2 / 2) * T) / (v * T^0.5) d2 = d1 - (v * T^0.5) where rho...

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Generalized Black-Scholes-Merton on Variance Form is an adaptation of the Black-Scholes-Merton Option Pricing Model including Numerical Greeks. The following information is an excerpt from Espen Gaarder Haug's book "Option Pricing Formulas". This version is to price Options using variance instead of volatility. Black- Scholes- Merton on Variance Form In some...

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Asay (1982) Margined Futures Option Pricing Model is an adaptation of the Black-Scholes-Merton Option Pricing Model including Analytical Greeks and implied volatility calculations. The following information is an excerpt from Espen Gaarder Haug's book "Option Pricing Formulas". This version is to price Options on Futures where premium is fully margined. This...

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Black-76 Options on Futures is an adaptation of the Black-Scholes-Merton Option Pricing Model including Analytical Greeks and implied volatility calculations. The following information is an excerpt from Espen Gaarder Haug's book "Option Pricing Formulas". This version is to price Options on Futures. The options sensitivities (Greeks) are the partial derivatives...

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Garman and Kohlhagen (1983) for Currency Options is an adaptation of the Black-Scholes-Merton Option Pricing Model including Analytical Greeks and implied volatility calculations. The following information is an excerpt from Espen Gaarder Haug's book "Option Pricing Formulas". This version of BSMOPM is to price Currency Options. The options sensitivities...

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Generalized Black-Scholes-Merton w/ Analytical Greeks is an adaptation of the Black-Scholes-Merton Option Pricing Model including Analytical Greeks and implied volatility calculations. The following information is an excerpt from Espen Gaarder Haug's book "Option Pricing Formulas". The options sensitivities (Greeks) are the partial derivatives of the...