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Here the price of the option is its discounted expected value; see risk neutrality and rational pricing. The technique applied then, is (1) to generate a large number of possible, but random , price paths for the underlying (or underlyings) via simulation , and (2) to then calculate the associated exercise value (i.e. "payoff") of the option ...
Under the risk neutrality assumption, today's fair price of a derivative is equal to the expected value of its future payoff discounted by the risk free rate. Therefore, expected value is calculated using the option values from the later two nodes ( Option up and Option down ) weighted by their respective probabilities—"probability" p of an ...
The terms and are put in by-hand and represent factors that ensure the correct behaviour of the price of an exotic option near a barrier: as the knock-out barrier level of an option is gradually moved toward the spot level , the BSTV price of a knock-out option must be a monotonically decreasing function, converging to zero exactly at =. Since ...
In mathematical finance, Margrabe's formula [1] is an option pricing formula applicable to an option to exchange one risky asset for another risky asset at maturity. It was derived by William Margrabe (PhD Chicago) in 1978. Margrabe's paper has been cited by over 2000 subsequent articles.
This extra money is for the risk which the option writer/seller is undertaking. This is called the time value. Time value is the amount the option trader is paying for a contract above its intrinsic value, with the belief that prior to expiration the contract value will increase because of a favourable change in the price of the underlying asset.
Risk-free rate: The rate of return on the riskless asset is constant and thus called the risk-free interest rate. Random walk: The instantaneous log return of the stock price is an infinitesimal random walk with drift; more precisely, the stock price follows a geometric Brownian motion , and it is assumed that the drift and volatility of the ...
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The Black formula is similar to the Black–Scholes formula for valuing stock options except that the spot price of the underlying is replaced by a discounted futures price F. Suppose there is constant risk-free interest rate r and the futures price F(t) of a particular underlying is log-normal with constant volatility σ.
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