1. Examples (Options) Description:
The floating strike look back call gives the owner the right to buy the underlying S at the lowest price of the underlying that was observed during the options lifetime T. The floating strike look back put gives the owner the right to sell the underlying at the highest price.
Black-Scholes Price:
where:

2. Modelling using ThetaML
Examples (Options)
Modelling using ThetaML T
P=max(S-Smin*EUR,0) dt
Smin=min(S/EUR,
Smin)

3. Examples (Options) ThetaScript Model FSLB import S "Underlying stock"
import EUR "Numeraire"
export V "Option value"
s_min= S/EUR
Theta 1
s_min=min(S/EUR,s_min)
V= max(S -s_min*EUR,0)
end

4. Number of Monte Carlo simulations:1000 random_seed:varied from 1..100
Examples (Options)
Configuration:
Number of Monte Carlo simulations:1000
random_seed:varied from
Input Parameter
Black-Scholes Price P=

5. Examples (Options) Description:
The floating strike Asian option has a payoff based on the difference between the underlying at the expiration(S) and the average of the underlying prior to the expiration.

6. Modelling using ThetaML
Examples (Options)
Modelling using ThetaML T
av=sum/n
P=max(S-av*EUR,0) dt
sum=sum+S/EUR
n=n+1

7. Examples (Options) ThetaScript Model Asian import S "Underlying stock"
import EUR "Numeraire"
export V "Option value"
sum=0
n=0
loop 250
Theta 0.04
n=n+1
sum=sum+S/EUR
end
av=sum/n
V= max(S-av*EUR,0)

8. Examples (Options)
Configuration:
Number of Monte Carlo simulations:1000
random_seed:varied from
Input Parameter

9. Examples (Options) Description:
The European option have a payoff at maturity based on the underlying at the expiration(S) and Strike price(K). Some examples of European options are:
1. European Call
2. European Put.
3. Binary cash-or-nothing etc.
For particular example of European option we look at binary cash-or-nothing.
The binary cash-or-nothing option pays a fixed cash amount if the option expires in the money and nothing otherwise.
Black-Scholes Price:
where:

10. Modelling using ThetaML
Examples (Options)
Modelling using ThetaML
P=Cash Y
S>K T N
P=0

11. Examples (Options) ThetaScript Model Binary
import S "Underlying stock"
import C "Cash"
import K "Strike"
export V "Option value"
Theta 1
if (S-K)>0
V= Cash
else
V=0
end

12. Examples (Options)
Input Parameter
Black-Scholes Price P=

13. Examples (Options) Description:
A cliquet or ratchet option is a series of at the money options, with periodic settlement, resetting the strike value at the then current price level, at which time, the option locks in the difference between the old and new strike and pays that out as the profit. The profit can be accumulated until final maturity, or paid out at each reset date.

14. Modelling using ThetaML
Examples (Options)
Modelling using ThetaML
V=N*EUR*max(Fg,min(Cg,sum))
Sum = 0 T
S_EUR = S/EUR
Sum= Sum+Z dt R=
(S/EUR-S_EUR)/S_EUR
Z=max(Fl,min(Cl,R))

15. Examples (Options) ThetaScript Model Cliquet
import S "Underlying stock"
import N "Notional"
import Cg “Global Cap”
import Cl “local Cap”
import Fg “Global Floor”
import Fl “Local Floor”
export V "Option value"
sum=0
loop 5
S_EUR=S/EUR
Theta 1
R=(S/EUR-S_EUR)/S_EUR
Z=max(Fl,min(Cl,R))
sum=sum+Z
end
V=N*EUR*max(Fg,min(Cg,sum))

16. Examples (Options) Input Parameter Result: Reference:
Numerical Methods and Volatility Models for Valuing Cliquet Options.
H.A. Windcliff P.A. Forsyth K.R.Vetzal
Jump diffusion model