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
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.