How to price December 2020 maturity European call option of S&P 500 (Strike of 3000). What should be the risk free rate ?
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How does the option being longer-dated play a special role in your question? – LocalVolatility May 02 '18 at 18:52
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This has been discussed before here (https://quant.stackexchange.com/questions/33776/why-must-the-risk-free-rate-be-free-from-risk-in-risk-neutral-valuation/33778#33778) and here (https://quant.stackexchange.com/questions/32239/which-risk-free-interest-rate-to-use-in-black-scholes-equation/38557#38557). Particularly, the former discusses how "risk-free" pertains to funding costs. In short, while there is no such thing as a risk-free rate of return, the writer's cost of collateral is probably the closest thing. What would your broker charge for collateral over the life of the option? – David Addison May 02 '18 at 19:34
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Thanks David for your answer. I got your point and will use collateral rate for 32 month maturity. If suppose I prefer to use OIS spread or US T bill what rate should I consider it to be for 32 Month maturity. Also, I have priced this option as per BS calculation it turned out to be 72.50/- what is your view on this calculation. – Add May 02 '18 at 19:47