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.


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

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  • $\begingroup$ 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