Option Pricer

This is a Python project made to apply what I've learned about option pricing during my MSc in Finance.

References

1. Hull, J. (2014) Options, Futures and Other Derivatives. 9th Edition
2. A Black–Scholes user’s guide to the Bachelier model: https://arxiv.org/pdf/2104.08686.pdf
3. Iacus, S.M. (2011) Option Pricing and Estimation of Financial Models with R

How to run

1. Clone the repository or download it as ZIP file
2. Run pip install -r requirements.txt (optional)
3. Run main.py [arguments]

Requirements

• numpy
• scipy
• matplotlib

Usage

• Supported underlying assets:
  • Dividend and non-dividend paying stocks
  • Currencies
  • Commodities
  • Futures

Argument	Description
h	Print help message
m	Pricing Method Black-Scholes model, -m BS Bachelier model, -m BA Binomial Tree, -m BT Monte Carlo Simulation, -m MC
p	Product. The option type to price: European options: EUC (call), EUP (put) American options: USC (call), USP (put) Futures-style options: FSTYLEC (call), FSTYLEP (put) Bond options: BC (call), BP (put)
s	Spot Price
f	Forward Price
k	Strike Price
r	Annualized Risk Free Rate
rf	Annualized Foreign Risk Free Rate
u	Annualized Storage Cost
q	Annualized Dividend Yield
d	Dividends. List of expected discrete dividends. e.g. three semi-annual dividends of 0.5$: -d 0.5 0.5 0.5
dt	Dividend Times. It refers to the times in which the dividends will be paid. In the example above we'll set: -dt 0.5 1 1.5
t	Time to Expiration. It can be expressed in different ways: Years, using only a float value e.g. -t 1 Months, by adding "m" or "months" to a number e.g -t 12 m Weeks, by adding "w" or "weeks" e.g. -t 52 w Days, by adding "d" or "days" e.g. -t 252 d
vol	Annualized Log-Normal Volatility. The volatility used in Black-Scholes model and Binomial Trees.
nvol	Annualized Normal Volatility. The volatility used in the Bachelier model. If it isn't included when the Bachelier pricing model is selected, the tool will automatically convert log-normal volatility in normal volatility.
b	Current Bond Cash Price
i	PV of Bond's Income
steps	Number of Steps. Number of steps to use in the binomial tree.
print	Print the Binomial Tree
greeks	Print the Values of Delta, Theta, Gamma, Vega and Rho
n	Number of Simulations
process	Underlying process Geometric Brownian Motion, -process GBM Variance-Gamma Process, -process VG Merton Jump Process, -process MJ
params	List of Process' Parameters. e.g. jumps' intensity, mean and standard deviation of jumps' distribution

Examples

European option

A financial institution has just sold 1,000 seven-month European call options on the Japanese yen. Suppose that the spot exchange rate is 0.80 cent per yen, the exercise price is 0.81 cent per yen, the risk-free interest rate in the United States is 8% per annum, the risk-free interest rate in Japan is 5% per annum, and the volatility of the yen is 15% per annum. Calculate the delta, gamma, vega, theta, and rho of the financial institution’s position. Interpret each number

Black-Scholes

Input:

python main.py -p EUC -s 0.8 -k 0.81 -r 0.08 -rf 0.05 -vol 0.15 -t 7 m -greeks

Output:

INFO - pricers - Pricing using Black-Scholes
INFO - main - The option price is: 0.03741
INFO - main - The Greeks are: Theta -0.03989 | Delta 0.52493 | Gamma 4.20593 | Vega 0.23553 | Rho 0.22315

Bachelier

Input:

python main.py -p EUC -s 0.8 -k 0.81 -r 0.08 -rf 0.05 -vol 0.15 -t 7 m -m BA

Output:

INFO - pricers - Pricing using Bachelier
INFO - main - The option price is: 0.03751

Monte Carlo Simulation under GBM

Input:

python main.py -p EUC -s 0.8 -k 0.81 -r 0.08 -rf 0.05 -vol 0.15 -t 7 m -m MC -n 5000

Output:

INFO - pricers - Pricing using Monte Carlo Simulation
INFO - pricers - Pricing under Geometric Brownian Motion
INFO - main - The option price is: 0.03679

Monte Carlo Simulation under Variance-Gamma process

Input:

python main.py -p EUC -s 0.8 -k 0.81 -r 0.08 -rf 0.05 -vol 0.15 -t 7 m -m MC -n 5000 -process VG -params 0.02 1

Output:

INFO - pricers - Pricing using Monte Carlo Simulation
INFO - pricers - Pricing under Variance Gamma Process
INFO - main - The option price is: 0.04568

European option (dividend)

Consider a European call option on a stock when there are ex-dividend dates in two months and five months. The dividend on each ex-dividend date is expected to be $0.50. The current share price is $40, the exercise price is $40, the stock price volatility is 30% per annum, the risk-free rate of interest is 9% per annum, and the time to maturity is six months.

Input:

python main.py -p EUC -d 0.5 0.5 -dt 0.16667 0.41667 -s 40 -k 40 -vol 0.3 -r 0.09 -t 0.5

Output:

INFO - pricers - Pricing using Black-Scholes
INFO - main - The option price is: 3.67123

Futures-style option

The strike price of a futures option is 550 cents, the risk-free rate of interest is 3%, the volatility of the futures price is 20%, and the time to maturity of the option is 9 months. The futures price is 500 cents ... (d) What is the futures price for a futures style option if it is a call?

Input:

python main.py -p FSTYLEC -f 5 -k 5.5 -r 0.03 -vol 0.2 -t 0.75

Output:

INFO - pricers - Pricing using Black-Scholes
INFO - main - The option price is: 0.16564

Bond option

Use the Black’s model to value a one-year European put option on a 10-year bond. Assume that the current value of the bond is $125, the strike price is $110, the one-year risk-free interest rate is 10% per annum, the bond’s forward price volatility is 8% per annum, and the present value of the coupons to be paid during the life of the option is $10

Input:

python main.py -p BC -b 105 -i 34.968 -r 0.1 -t 4 -vol 0.02 -k 100

Output:

INFO - pricers - Pricing using Black-Scholes
INFO - main - The option price is: 3.19007

American Option

Three-step tree to value an American 9-month put option on a futures contract when the futures price is 31, strike price is 30, risk-free rate is 5%, and volatility is 30%

Input:

python main.py -m BT -steps 3 -p USP -f 31 -k 30 -r 0.05 -vol 0.3 -t 9 m -print

Output:

INFO - pricers - Pricing using Binomial Tree
INFO - main - The option price is: 2.83564