# Difference between Black-Scholes and Garman Kohlhagen formula

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## Garman Kohlhagen Model in VBA

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Further details on this and other support available from us is given on our website. Hi Can someone tell me the difference between the Black-scholes formula in Chapter 12 and Garman-Kohlhagen formula on pg 47 in the formula book?

Why is the r and q 'missing' from Black-scholes formula? In what case do I use Black-scholes or Garman-Kohlhagen? Thank you very much. They are two different but related beasts. Assume for a moment that there is a function that gives you the price of a call option. The B-S equation is simply an equation that any such function must satisfy or bad things, such as arbitrage, happen.

The G-K function is a function that can be shown to satisfy the B-S equation, and therefore it can be used to give the price of a call option. I don't have notes in front of me, but I think q is left out of the derivation for simplicity, but r should be used in B-S unless the derivation is assuming a zero risk rate.

Most trading is over the counter OTC and is lightly regulated, but a fraction is traded on exchanges like the International Securities Exchange , Philadelphia Stock Exchange , or the Chicago Mercantile Exchange for options on futures contracts.

In this case the pre-agreed exchange rate , or strike price , is 2. If the rate is lower than 2. The difference between FX options and traditional options is that in the latter case the trade is to give an amount of money and receive the right to buy or sell a commodity, stock or other non-money asset.

In FX options, the asset in question is also money, denominated in another currency. For example, a call option on oil allows the investor to buy oil at a given price and date. The investor on the other side of the trade is in effect selling a put option on the currency.

To eliminate residual risk, match the foreign currency notionals, not the local currency notionals, else the foreign currencies received and delivered don't offset. Corporations primarily use FX options to hedge uncertain future cash flows in a foreign currency. The general rule is to hedge certain foreign currency cash flows with forwards , and uncertain foreign cash flows with options. This uncertainty exposes the firm to FX risk.

This forward contract is free, and, presuming the expected cash arrives, exactly matches the firm's exposure, perfectly hedging their FX risk. If the cash flow is uncertain, a forward FX contract exposes the firm to FX risk in the opposite direction, in the case that the expected USD cash is not received, typically making an option a better choice.

As in the Black—Scholes model for stock options and the Black model for certain interest rate options , the value of a European option on an FX rate is typically calculated by assuming that the rate follows a log-normal process.

In Garman and Kohlhagen extended the Black—Scholes model to cope with the presence of two interest rates one for each currency.

The results are also in the same units and to be meaningful need to be converted into one of the currencies. A wide range of techniques are in use for calculating the options risk exposure, or Greeks as for example the Vanna-Volga method.