Option valuation

Before discussing how options can be valued, we need to be able to distinguish the different types of options that are traded in financial markets. In general, options (when bought) provide the right to buy or sell and asset at a certain price fixed now at (or before) some date in the future. The value of option contracts is thus always as least as high as, and often higher than that of forward contracts. This is because forward contracts are an obligation to buy or sell whereas options provide a right.

Call and put options

Call options provide the buyer the right to buy a certain asset at a price fixed before (or on) expiration of the option contract. Call options can thus be used as an alternative to buying shares when having bullish expectations. Put options, on the other hand, provide the buyer a right to sell a certain asset at a price fixed before (or on) expiration of the option contract. Put options can thus be used to buy protection for shares you own, or to speculate on a downward market. The seller of either call or put options is thus obliged to sell (in case of call options) or buy (in case of put options) the underlying securities when asked to. In exchange for assuming this risk, the option seller receives a premium from the option buyer (i.e. the option price).

European, American and Bermudan options

The option style is important, both for valuation purposes as well as for risk management. The option style refers to when option buyers can exercise their options. European style options are the most simple. These options can only be exercised at maturity. American-style options on the other hand can be exercised at or before maturity. As a result, American-style options are (most of the time but no always) worth than European option. Bermudan options lie somewhere in between European- and American-style options. Bermudan options can be exercised at maturity or at certain fixed dates, and therefore not at every point in time between now and expiry.

Asian options

Asian options provide a payoff at maturity that is a function of the average price it realized during a certain period, over a particular threshold. As a result of its backward-looking nature, simulation methods are needed to value Asian options.

Binary options

Binary options provide a fixed payoff. Either the buyer (long binary) obtains nothing if the price at maturity is not higher than the strike price, or the buyer receives a fixed amount if the price ends up above the strike price. The exact amount by which the closing price exceeds the strike price is not important here. Whether it is 1 cent, 1 dollar, or 10 dollar does not affect the cashflow received. Because of its odd payoff structure, binary options are strongly related to pure speculation or gambling.

Lookback options

Lookback options are a partical kind of exotic options that provide at maturity a payoff in function of the most favorable realized price over a certain period. Due to their floating strike price, these kind of options always end up in the money and are thus more expensive.

  • Binomial model

    The binomial model enables investors to get some intuition on how options can be priced. The binomial model is able to value both European style options as well as American style options.

  • Black Scholes option pricing model

    The Black and Scholes option pricing model provides an analytical solution that allows us to value European-style call- and put options. The model can be used both for  non-dividend paying as well as dividend paying securities.

  • Warrant valuation

    Warrants are a somewhat peculiar type of derivatives that nevertheless behave similarly as options. However, unlike options, warrants are issued by companies to attract funding, or to increase the attractiveness of other securities issued by companies (e.g. bonds).

  • Asian option valuation

    Asian options differ in payoff calculation from European and American option. The payoff for an Asian option equals the average price realized minus the strike (call) or the strike minus the average price realized.

  • Binary option pricing

    The payoff of binary options differs considerably from that of regular options. Binary options either have a fixed positive payoff or no payoff at all. As a result of this particular nature of the binary options’ payoff, trading binary options is often seen as speculation or gambling.

  • Lookback option pricing

    A lookback option offers the holder the right to buy a certain asset at the lowest price realized during a certain period. Therefore, thus called lookback option. In case of a put, it offers the holder to sell a certain asset at the highest price realized during a certain period.

Summary

There exist a huge amount of different option types in the market. With respect to option exercise, options can either be European, American or Bemudan style. All of these can be either cal or put options, which can be bought or sold. Among the exotic option family, binary options and Asian options are the most commonly known.

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