On 9/15/2022, you collect the closing price of each asset:

Asset	Closing Price
TSLA	303.75
S&P 500	3,901.35
EUR/USD	0.9984

You also know that the 3-month SOFR is 3.44% per year whereas the 3-month Euribor reference rate is 1.10% per year. All rates are expressed with continuous compounding and you can assume that they stay constant at all periods in your tree.

Build an n-period binomial tree for TSLA, the S&P 500 and the EUR/USD exchange rate as of 9/15/2022. On Canvas, you will find a grade for an assignment called Number of Periods. Use this number as your value for n. To compute up and down movements for each period, use u=et and d=1/u, where t=T/n, T=3/12, and is the annualized volatility that you computed in Problem 1. That is, your tree will span a period of 3 months. You will use the binomial trees to compute the values of the options described below.

Compute the price of at-the-money European call and put options as of 09/15/2022 written on TSLA and expiring in 3-months. Express the price of each option per share.

Compute the price of at-the-money European call and put options as of 09/15/2022 written on the S&P 500 and expiring in 3-months. SPX options are cash settled and their payoffs are equal to $100max(SK,0) for calls, and $100max(KS,0) for puts, where S is the value of the index at expiration. In your computations use a dividend yield of 1.52% per year expressed with continuous compounding.

Compute the price of 3-month at-the-money European call and put options as of 09/15/2022 written on the EUR/USD over a notional of EUR 1,000,000.