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For a non-dividend paying share of a company whose price at time t is denoted by St, the current price of the share is ${S0 = £100}$. In any year the volatility is $20\%$ (price of the share can either increase by $20\%$ or decrease by $20\%$). The continuously compounded constant annual risk-free interest rate is $r$, such that $e^r = 1.1$

The maturity payoff for a $2$ year derivative contract is

$${S2 \times I(S2 > 90)};$$

(the option striking price is ${£}90$ and ${I(S2 > 90)}$ is the indicator function, i.e. $ I(S2 > 90) = 1\; \text{if} \;S2 > K, 0 \;\text{if} \;S2 ≤ 90)$

How do I determine the current price of the derivative?

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    You should call a broker ask for the current price. The price of a derivative is what the market decides it is, regardless of what the Black-Scholes theory says it should be. Computing a value for the option using the standard formulas is a very easy homework exercise. – 2017-02-25
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    @brian-borchers Once I've used the Black-Scholes formula to obtain a value for the theoretical call premium, how do I use that to find the current price of the derivative? – 2017-02-25
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    The Black-Scholes formula will tell you what the price of the derivative should be if the assumptions of the model are met. Probably, your instructor wants you to apply the formula and report that answer. My point was that in practice, actual prices for derivatives often are somewhat different from what the theory would predict and that problems with the assumptions (what's the correct risk-free interest rate to use) can cause problems. – 2017-02-25
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    @BrianBorchers So it's just a case of using the BS formula, I understand now, thank you So if the payoff was K × I (S2 > K), and K is 90 again, do I adjust the formula to get the result, or do I do something else? – 2017-02-26

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