在黑人學術方程中使用的無風險利率
對不起，但我是眾多的量化金融。根據BS推導，無風險的利率是特定投資率傾向於何時風險趨於零。假設我想用固定的罷工價格和成熟的選擇購買，這是我必須進入等式的速度？為什麼？
理論上， is a short-term safe interest rate, and it is constant through time though the theory does goes through with (average from to ) in place or . In practice, you take the continuously compounded yield on a T-bill of maturity closest to that of your option. Eurocurrency rates work too, especially for currency options. In theory, you should choose whether to use a LIBOR or LIBID rate depending upon whether the option dealer who delta hedges your trade is going to be borrowing money (at the LIBOR rate) or lending money (at the LIBID rate).
Source: Basic Black-Scholes: Option Pricing and Trading (2’nd edition) by Timothy Falcon Crack, p. 143.
Most option trades are collateralized. In that case, the correct rate to use for discounting is the rate earned by the collateral, or a mix of the collateral rate and risk-free rate for partial collateralization. You still need to pay attention that the stock forward level is priced correctly, so use a stock repo rate or similar backed out from call/put parity in the options market or data from futures or forwards.
See <http://www.math.columbia.edu/~fts/What%20Rate%20to%20use%20v1.pdf>