| Title: | Pricing of Different Types of Call |
|---|---|
| Description: | Compute the price of different types of call using different methods. The types available are Vanilla European Calls, Vanilla American Calls and American Digital Calls. Available methods are Montecarlo Simulation, Montecarlo Simulation with Antithetic Variates, Black-Scholes and the Binary Tree. |
| Authors: | Elia Degiorgi, Federico Milan, Davide Zaramella, Valerija Stoeva |
| Maintainer: | Elia Degiorgi <[email protected]> |
| License: | GPL-3 |
| Version: | 1.0 |
| Built: | 2024-11-09 06:18:40 UTC |
| Source: | CRAN |
Compute the price of different types of call using different methods. The types available are Vanilla European Calls, Vanilla American Calls and American Digital Calls. Available methods are Montecarlo Simulation, Montecarlo Simulation with Antithetic Variates, Black-Scholes and the Binary Tree.
Elia Degiorgi, Federico Milan, Davide Zaramella, Valerija Stoeva
Maintainer: Elia Degiorgi <[email protected]>
"Option Pricing Using Different Techniques" by Degiorgi Elia, Milan Federico, Zaramella Davide, Stoeva Valerija (2019)
MontecarloCalls(10,11,1,0.05,0.2,100) MontecarloAntitheticCalls(10,11,1,0.05,0.2,100) BlackscholesCalls(10,11,1,0.05,0.2) AmericanDigitalCalls(10,11,1,0.05,0.2,"A") AmericanDigitalCalls(10,11,1,0.05,0.2,"C")MontecarloCalls(10,11,1,0.05,0.2,100) MontecarloAntitheticCalls(10,11,1,0.05,0.2,100) BlackscholesCalls(10,11,1,0.05,0.2) AmericanDigitalCalls(10,11,1,0.05,0.2,"A") AmericanDigitalCalls(10,11,1,0.05,0.2,"C")
Digital options, also called binary option, are options which pay a fixed payoff when the underlying stock price crosses the strike price. Thus, American Digital Options are automatically exercised as soon as they get in the money. In addition, American Digital options can be splitted in two categories: cash-or-nothing (which pays a fixed payoff in case of the underlying stock price ends up in the money) and asset-or-nothing (which pays the value of the underlying stock in case of the underlying stock price ends up in the money) options.
AmericanDigitalCalls(s0, k, t, r, vol, call_type)AmericanDigitalCalls(s0, k, t, r, vol, call_type)
s0 |
stock price at time 0 |
k |
strike price |
t |
time to maturity in years |
r |
annual interest rate |
vol |
annual volatility |
call_type |
"A":asset or "C":cash |
No details
Price of the call
Be sure that the type of the call is "A" or "C". All input values must be stricly positive.
Degiorgi Elia, Milan Federico, Zaramella Davide, Stoeva Valerija
"Option Pricing Using Different Techniques" by Degiorgi Elia, Milan Federico, Zaramella Davide, Stoeva Valerija (2019)
AmericanDigitalCalls(10,11,1,0.05,0.2,"A") # 4.277183AmericanDigitalCalls(10,11,1,0.05,0.2,"A") # 4.277183
The Binomial Option Pricing Model is a method which uses an iterative procedure to evaluate options. Based on a discrete time interval and a multi-period approach, the model evaluates each time the option generating an upward or downward movement of the underlying price. In each node the price of the option can take only two values: the first one corresponds to the probability that the price of the option goes up whereas the second one corresponds to the probability that the price drops.
BinaryTreeCalls(s0, k, r, vol, deltaT, nsteps)BinaryTreeCalls(s0, k, r, vol, deltaT, nsteps)
s0 |
stock price at time 0 |
k |
strike price |
r |
annual interest rate |
vol |
annual volatility |
deltaT |
time variation in years |
nsteps |
number of steps |
No details
Price of the call
All input values must be stricly positive.
Degiorgi Elia, Milan Federico, Zaramella Davide, Stoeva Valerija
"Option Pricing Using Different Techniques" by Degiorgi Elia, Milan Federico, Zaramella Davide, Stoeva Valerija (2019)
BinaryTreeCalls(10,11,0.05,0.2,0.01,100) # 0.6053225BinaryTreeCalls(10,11,0.05,0.2,0.01,100) # 0.6053225
Black-Scholes is a model used to price Vanilla European Options assuming that the market is free from arbitrage and the underlying asset price follows a geometric Brownian motion. In other words, it assumes that the underlying stock price follows a random walk and it partially satisfies the efficient market hypothesis.
BlackscholesCalls(s0, k, t, r, vol)BlackscholesCalls(s0, k, t, r, vol)
s0 |
stock price at time 0 |
k |
strike price |
t |
time to maturity in years |
r |
annual interest rate |
vol |
annual volatility |
No details
Price of the call
All input values must be stricly positive.
Degiorgi Elia, Milan Federico, Zaramella Davide, Stoeva Valerija
"Option Pricing Using Different Techniques" by Degiorgi Elia, Milan Federico, Zaramella Davide, Stoeva Valerija (2019)
BlackscholesCalls(10,11,1,0.05,0.2) # 0.6040088BlackscholesCalls(10,11,1,0.05,0.2) # 0.6040088
The Antithetic Variates is a method which decreases the approximation error by reducing the variance of the simulation result.
MontecarloAntitheticCalls(s0, k, t, r, vol, n)MontecarloAntitheticCalls(s0, k, t, r, vol, n)
s0 |
stock price at time 0 |
k |
strike price |
t |
time to maturity in years |
r |
annual interest rate |
vol |
annual volatility |
n |
number of simulations |
No details
Price of the call
Degiorgi Elia, Milan Federico, Zaramella Davide, Stoeva Valerija
"Option Pricing Using Different Techniques" by Degiorgi Elia, Milan Federico, Zaramella Davide, Stoeva Valerija (2019)
MontecarloAntitheticCalls(10,11,1,0.05,0.2,100) # 0.5749907MontecarloAntitheticCalls(10,11,1,0.05,0.2,100) # 0.5749907
Montecarlo is a method used to price options. It computes the expected value of the price with respect to an underlying probability distribution which is assumed to be a Gaussian stochastic process described by a geometric Brownian motion.
MontecarloCalls(s0, k, t, r, vol, n)MontecarloCalls(s0, k, t, r, vol, n)
s0 |
stock price at time 0 |
k |
strike price |
t |
time to maturity in years |
r |
annual interest rate |
vol |
annual volatility |
n |
number of simulations |
No details
Price of the call
Degiorgi Elia, Milan Federico, Zaramella Davide, Stoeva Valerija
"Option Pricing Using Different Techniques" by Degiorgi Elia, Milan Federico, Zaramella Davide, Stoeva Valerija (2019)
MontecarloCalls(10,11,1,0.05,0.2,100) # 0.6164035MontecarloCalls(10,11,1,0.05,0.2,100) # 0.6164035