For a European call option on a nondividend paying stock with 1 year to expiry:
a) Stock follows Black Scholes framework
b) price of stock =40
c) strike price = 50
d) Γ is .0425
e) continuously compounded risk-free interest rate is .07
The price of the stock jumps to 40.50 and the price of the option increases by .0915. Determine the implied volatility of the stock based on the delta-gamma approximation.
I use the formula:
C(S1) = C(S0) + Δ* Є + .5* Γ*( Є^2) + error term
In the book for the solution, they use this formula as well, however they have C(S0) = 0:
.0915 = .1724*.5 + .5*.0425*(.5^2)
where
Δ=.1724
Є = .5
How do we know C(S0) =0?
a) Stock follows Black Scholes framework
b) price of stock =40
c) strike price = 50
d) Γ is .0425
e) continuously compounded risk-free interest rate is .07
The price of the stock jumps to 40.50 and the price of the option increases by .0915. Determine the implied volatility of the stock based on the delta-gamma approximation.
I use the formula:
C(S1) = C(S0) + Δ* Є + .5* Γ*( Є^2) + error term
In the book for the solution, they use this formula as well, however they have C(S0) = 0:
.0915 = .1724*.5 + .5*.0425*(.5^2)
where
Δ=.1724
Є = .5
How do we know C(S0) =0?
Exercise 12.19 in ASM Manual
0 commentaires:
Enregistrer un commentaire