# swap discrete market model

Let be $$M = (S_0,E,\Phi)$$ a market where the risk-free rate is $$r = 0$$ and the Euribor $$E$$ evolves (annually) in discrete time following a three-period binomial model. Assume that $$E_0 = 0.031$$, the multiplicative parameters are $$u = 1.03$$ and $$d = 0.71$$ with a risk neutral probability of an up movement equal to $$p = 0.74$$. Consider an exotic Interest rate Swap with unit notional, semestral payments and maturity 3 years, whose floating leg pays 0.018 (annual) if Euribor lies under the bound $$s = 0.01$$ (annual) at the payment date while it pays the Euribor rate plus a spread of 0.007 (annual) if the Euribor lies above or it is equal to the bound $$s$$. Recover the swap rate assuring the absence of arbitrage opportunities.

I have the text of this exercise, I tried to change the numeraire in order to have the probability of up and down movement consistent with the risk neutral probability $$p = 0.74$$. My results are $$\text{up} = 1.2246$$ and $$\text{down} =$$0.3606\$. In this way the Euribor goes under the critical value 0.01 and I can compute the swap payments, but since that the down movement is too low I have the doubt that I am wronging the way to solve the exercise.

Can someone confirm that this is the correct way or give me some advise in order to solve it? Thank you in advance.

I’m sorry in case is a simple-minded question but I am a beginner.

In case you have problem with the notation, $$S_0$$ is the risk-free asset and $$E_0$$ the Euribor than the risky asset.