Black Scholes Pricing Option Formulae

sunandaC

New member
The Black–Scholes formulas for the prices of European calls and puts on a non-dividend paying stock are:

C = SN(d1) – Xe-rT N(d2)

P = Xe-rT N(-d2)- SN(-d1)

Where d1 = [ ln s/x +(r+δ2/2)T ]/ δ √T

And d2 = d1 –δ√T

• The Black Scholes equation is done in continuous time. This requires continuous compounding. The “ r ” that in this is ln(1+r). E.g. if the interest rate per annum is 12%, you need to use ln1.12 or 0.1133, which is continuously compounded equivalent of 12% per annum.

• N () is the cumulative normal distribution. N(d1 ) is called the delta of the option which is a measure of change in option in option price with respect to change in the price of the underlying asset.

• δ a measure of volatility is the annualized standard deviation of continuously compounded returns on the underlying. When daily sigma are given, they need to be converted into annualized sigma.

• Σ annual = Σ daily * √number of trading days per year. On a average there are 250 trading days in a year.

• X is the exercise price, S is the spot price and T the time to expiration.
 

rosemarry2

MP Guru
The Black–Scholes formulas for the prices of European calls and puts on a non-dividend paying stock are:

C = SN(d1) – Xe-rT N(d2)

P = Xe-rT N(-d2)- SN(-d1)

Where d1 = [ ln s/x +(r+δ2/2)T ]/ δ √T

And d2 = d1 –δ√T

• The Black Scholes equation is done in continuous time. This requires continuous compounding. The “ r ” that in this is ln(1+r). E.g. if the interest rate per annum is 12%, you need to use ln1.12 or 0.1133, which is continuously compounded equivalent of 12% per annum.

• N () is the cumulative normal distribution. N(d1 ) is called the delta of the option which is a measure of change in option in option price with respect to change in the price of the underlying asset.

• δ a measure of volatility is the annualized standard deviation of continuously compounded returns on the underlying. When daily sigma are given, they need to be converted into annualized sigma.

• Σ annual = Σ daily * √number of trading days per year. On a average there are 250 trading days in a year.

• X is the exercise price, S is the spot price and T the time to expiration.

Hello friend,

Here I am uploading White paper on Black-Scholes Model and Extensions by Evan Turner, so please download and check it.
 

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