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On 24th Feb 2017, you collected data on European-style put options written on the S&P500 index, which mature on 30th June 2017. You may assume
On 24th Feb 2017, you collected data on European-style put options written on the S&P500 index, which mature on 30th June 2017. You may assume the time till expiry is 0.3492 years. On 24th Feb 2017 the S&P 500 index was at 2367.34. The price of a zero coupon (US Government issued) bond paying 100 USD on 30th June 2017 was 99.6514 USD and the dividend yield on the S&P500 index was 1.92% per annum. Denote the annualized expected cum-dividend rate of return on the S&P 500 index on 24th Feb 2017 by . The date-1 Black-Scholes price of a European style put option (with strike K, expiration date T) on the S&P 500 is p = er(T-1) K N(-d2,1(r)) - e-(T-0), N(-d1,(r)), where q is the dividend yield (anmalized), r is the continuously compounded (annualized) risk-free rate, S, is the date t level of the the index. d(r) and de(r) are given by In(Kelante d1,4(3) + OVT-t, Ke d2.t() VT-7 and N'(x) = -x. The slope of the curve of put prices versus strike prices is related = t In ( Belo bagLOVT-t. = e
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