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I have the following question.

Suppose the price of a non-dividend paying share follows a quadrinomial model, where share price after 1 year can take one of the four possible values

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Let the continuously compounded annual risk-free rate of interest be 5%.

I have worked out the following assuming the volatility of the share price is $22.5\%$ and the Black-Scholes formula:

The price of a European call option with a strike of 12 and maturity in 1 year is $£0.41$.

The price of a European put option with strike of 8 and maturity in 1 year is $£0.11$.

Now I need to determine the values of $q_1,q_2,q_3$ and $q_4$ so that the quadrinomial tree is correctly calibrated to the current prices of the 3 assets.

I have only ever seen examples of this for a binomial tree and so I am stuck as to where to even start with this question.

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closed as unclear what you're asking by Raskolnikov, Xander Henderson, Aweygan, Learnmore, Saad Apr 3 '18 at 4:10

Please clarify your specific problem or add additional details to highlight exactly what you need. As it's currently written, it’s hard to tell exactly what you're asking. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question.

  • $\begingroup$ Your question is not clear at all. What are you trying to achieve? On the one hand you have a quadrinomial one-step tree, on the other hand you throw Black-Scholes around. Those are not the same thing. $\endgroup$ – Raskolnikov Apr 2 '18 at 20:16
  • $\begingroup$ Section a questions was to find the prices of the two European options using the black Scholes formula. Then the next question was using these two shares I have calculated and the one in the diagram, use calibration method to find the separate values of q $\endgroup$ – Lou Apr 3 '18 at 9:37