The UnRisk Language: Barrier Options

UnRisk code: click to enlarge

Let's assume we want to price a European up & out call option with the following properties:- The
spot price of the underlying equity is 100 EUR and the continuous dividends shall are 1%
- The lifetime of the option is 1 year
- The strike price is 100 EUR
- The barrier is 120 EUR
As long as the barrier has not been reached the option stays alive.

How can we translate this description into the language of UnRisk?
First, the underlying equity is constructed - this is done by the constructor MakeEquity. In the next
line it is shown how the barrier option is created. That's about it.

The next question is: How do I get a fair price for this option?
We need an interest rate curve (zero (yield) curve constructed from a given swap curve, i.e. bootstrapping).
We need volatility information about the underlying equity. This volatility information is available from the market as matrix of implied volatilities of vanilla options with different strikes (MyStrikes) and different remaining lifetimes (MyTerms).

But which volatility shall I choose?
Within UnRisk the user has 3 possibilities:
a) Use a flat volatility corresponding to the strike price and the expiry date of the considered option - i.e. the volatility corresponding to a strike price of 100 and a remaining lifetime of 365 days , which is 19.7%.
When using this volatility, the theoretical value of the barrier option is around 1.16588 EUR.
b) Take the whole volatility information and calibrate a volatility surface (i.e. following the Dupire approach).
When using this surface the theoretical value is 1.25375 EUR
c) New in UnRisk4 (coming this automn): Take the whole volatility information and calibrate a Heston model (i.e. use a stochastic volatility).
When using this model the theoretical value is 1.36714 EUR

UnRisk gives the user the possibility to valuate instruments under different models which helps him/her to analyse the risks of a financial instrument more carefully.

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