Ratio Tunnel Option Model
A ratio tunnel option is defined as a European vanilla option upon a European collar. It is another special case of a general compound option. We can get a close form pricing formula for the option on collar, or the ratio tunnel option. Most of results presented in the report can be applied here. Therefore, in the following, we just provided some specified information which is necessary in this case.
Our test cases cover currency pairs under European and American quoting conventions, and different call-put principal ratios. Risk numbers, including spot rate Delta’s, forward point Delta’s, Gamma’s, Vega’s, and Rho’s, as well as P/L’s have also been tested.
For an underlying collar, let us define Kc and Kp be the strikes of a call and a put in the collar, respectively, and Tclr be the maturity of the collar. Let T be the maturity of the ratio tunnel option where T < Tclr and PN be the notional principal of the option measured in the unit of an underlyer.
Then the matured payoff of the ratio tunnel call option at T can be given by
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