Funding in option pricing: the Black-Scholes framework extended
An option market-maker incurs funding costs when carrying and hedging inventory. Here, Wujiang Lou shows cash investing and borrowing at different rates and realistic non-zero repo haircuts can produce market-observed bid-ask spread levels for longer-term options
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The Black-Scholes (BS) option-pricing theory (Black and Scholes 1973; Merton 1973) has become the foundation of modern finance, in both theory and practice. A number of extensions have been developed either to relax assumptions or to deal with practical issues; for example, commodity options (Black 1976), American options on dividend-paying stocks (Barone-Adesi and Whaley 1987) and implied volatility smile (Derman 1994) via local or stochastic volatility (Dupire
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