Digital option formula

Digital option formula

Digital options (also known as binary options) have two general types cash-or-nothing or asset-or-nothing options. In the first type, a fixed amount of cash is paid at expiry if option is in-the-money, whilst the second pays out the value of the underlying asset.

To help understand the black-scholes formula for call and put options we start by looking at digital options. A digital call with a strike price kand maturity date tpays out one unit if s(t) k and nothing otherwise. Likewise a digital put with a strike price k and maturity date tpays out one unit if s(t) kand nothing otherwise.

1 digital options digital options have a payo v(ts t) ii fs t kgdomestic paying (15) w(ts t) s tii fs t kgforeign paying (16) in the domestic paying case the payment of the xed amount is in domestic currency, whereas in the foreign paying case the payment is in foreign currency.

  the outline of the paper is as follows in digital options section, we introduce digital options and their pricing formulas and we estimate it by using standard monte carlo. In modified monte carlo algorithm section, we propose the new monte carlo method based on the idea of using uniformly distributed random variable and the conditional exceedance probability.

A binary option (also known as an all-or-nothing or digital option) is an option where the payoff is either some amount or nothing at all. The payoff is, usually, a fixed amount of cash or the value of the asset. For our simulation, were going to look at cash-or-nothing binary options.

A digital call option (cash-or-nothing) can be replicated with two call options with different strike. When we make the delta infinitely small and assume we have arbitrary strike prices.

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Digital option formula

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