當時間單位為小時時,Black-Scholes公式是否起作用?


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根據布萊克-舒爾斯公式,時間單位通常以我所理解的年數為單位。我發現online calculator允許用戶輸入以天和年為單位的時間。

如果我要為時間變量插入例如1小時的公式,那麼首先將其轉換為年份,假設1小時大約是0.000114155年,該公式是否仍然正確?我會假設是的,但是我要問的原因是因為我使用上述計算器發現了這種情況。給定以下參數,計算器將返回調用值$ 7.81。

Calculation when the time units are in days.

但是,當我將時間單位更改為年,並將上述一小時的轉換值插入年時,通話價值下降為$ 7.00。為什麼會這樣呢?如果在較短的時間內發生看漲期權而不是在較長的時間內發生看漲期權,是否應該大幅度提高價格?

Calculation when the unit of time is in years, but the value for this parameter is one hour converted to years.

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I'm not sure what you're asking here quite, it seems to me that you are inputting a shorter time to maturity (from one day to one hour) and noticing a decrease in the contract value. Theta, the derivative of the option price with regards to time, is negative for for all options so this will always be the case no matter the time scale. Are you sure you have understood correctly what the Time to Expiration parameter in the formula means?

As an interesting side note I have seen the argument made that daily returns are normal by the CLT because they are made up of sum of many small price intraday changes that are I.I.D and come from some (any) distribution. So you could reason that because of this Black-Schooles framework would not hold when considering shorter time periods than this. This has however nothing to do with what you're confused about, I believe, even though that is how I originally interpreted your title.