Date	TSLA	SP500	EURUSD
1/3/2023	108.1	3824.14	1.067771
1/4/2023	113.64	3852.97	1.054685
1/5/2023	110.34	3808.1	1.060637
1/6/2023	113.06	3895.08	1.052222
1/9/2023	119.77	3892.09	1.065632
1/10/2023	118.85	3919.25	1.073318
1/11/2023	123.22	3969.61	1.073895
1/12/2023	123.56	3983.17	1.0766
1/13/2023	122.4	3999.09	1.086024
1/17/2023	131.49	3990.97	1.083013
1/18/2023	128.78	3928.86	1.079331
1/19/2023	127.17	3898.85	1.079785
1/20/2023	133.42	3972.61	1.083388
1/23/2023	143.75	4019.81	1.086508
1/24/2023	143.89	4016.95	1.087429
1/25/2023	144.43	4016.22	1.088815
1/26/2023	160.27	4060.43	1.092204
1/27/2023	177.9	4070.56	1.089443
1/30/2023	166.66	4017.77	1.087146
1/31/2023	173.22	4076.6	1.085069
2/1/2023	181.41	4119.21	1.086095

1. Using the Black-Scholes model and the annualized volatility computed in Problem 1, compute the price of European call and put options as of 4/5/2023 written on the S\&P 500, with strike K=4,110 and expiring in six 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 1.59% per year expressed with continuous compounding. 2. Using the Black-Scholes model and the annualized volatility computed in Problem 1, compute the price, delta, gamma, theta and vega of European call and put options as of 4/5/2023 written on the EUR/USD over a notional of EUR 1,000,000 with strike price K=$1.10 per Euro and expiring in six months