I have an excercise where we have two European Call Options, which have the same underlying, same maturity $t = 3$, same interest. The only difference is their price and their strike. The price of the first Call is $C_A = 3$ with a Strike of $K_A = 50$ and the second is $C_B = 12$ with Strike $K_B = 40$. Now I have to find out the maximal riskfree interest rate $r_f$. Does anyone how to find this $r_f$ thanks in advance
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1$\begingroup$ it's not obvious what you mean by 'max potential risk free interest rate' given the context you describe. please clarify your question. $\endgroup$ – Chris May 15 '19 at 21:18
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Consider the 40/50 call spread. This has a maximum payoff of 10, and hence has a maximum value of $$10/(1+r)^3$$. Where r is the annual risk free rate. But we know it is priced at 12-3 =9, so the maximal risk free rate satisfies $$(1+r)^3=10/9$$ which gives r= 3.6%
