Hedge pricing

Published

March 27, 2025

Calculate implied volatility

First we have to extract nifty data using tidyquant or Rquantlib.

Code 
# Install necessary packages if not already installed

# install.packages("quantmod")
# install.packages("RQuantLib")


# Load necessary packages

library(data.table)
library(tidyquant)

# Fetch the Nifty 50 index data
nifty_data <- tq_get("^NSEI", from = "1980-01-01", to = Sys.Date())

# Convert the data to a data.table
nifty_data <- data.table(nifty_data)

Get closing price

Code 
# Extract the last closing price directly from nifty_data
closing_price <- tail(nifty_data$close, 1)
closing_price
[1] 24768.3

Implied Volatility calculation

Plugin the latest option price for a liquid strike price with a 4 month maturity to get a reasonably accurate implied volatility.

Code 
library(quantmod)
library(RQuantLib)

# Define option parameters for a single observation
nifty_price<-23290.5
option_price <- 105  # Current market price of the option
strike_price <- 22500  # Strike price of the option
time_to_expiry <- 19/365  # Time to expiration in years
risk_free_rate <- 0.071   # Risk-free interest rate
volatility_guess <- 0.2  # Initial guess for the volatility

# Calculate implied volatility for a put option

vol<- EuropeanOptionImpliedVolatility(type = "put",value =option_price ,underlying = nifty_price,strike = strike_price,dividendYield = 0,riskFreeRate = risk_free_rate,maturity = time_to_expiry,volatility = .2)

vol
[1] 0.1903814
attr(,"class")
[1] "EuropeanOptionImpliedVolatility" "ImpliedVolatility"

At present the implied volatility is 19

Option pricing calculation

Aim for a strike less than 10 delta. Plugin the implied volatility and other data.

Code 
closing_price<-23389
strike <- closing_price * 0.85  # Strike price of the option
time_to_expiry <- 210/365  # Time to expiration in years
risk_free_rate <- 0.071   # Risk-free interest rate


price<-EuropeanOption(type = "put",underlying = closing_price,strike = strike,dividendYield = 0,riskFreeRate = risk_free_rate,maturity = time_to_expiry,volatility = vol)

cat("Closing price of nifty:\n")
Closing price of nifty:
Code 
print(closing_price)
[1] 23389
Code 
cat("Strike price:\n")
Strike price:
Code 
strike
[1] 19880.65
Code 
price
Concise summary of valuation for EuropeanOption 
    value     delta     gamma      vega     theta       rho    divRho 
 109.5493   -0.0693    0.0000 2363.9846 -268.4321 -995.5055  932.5147

Price of a 4 month 5 delta option is 110 for the given strike price

Take home message

Summary

Before buying hedge, plugin the market price, strike price, time to maturity, implied volatility and risk free rate to the BS formula and find out the fair value. Then only buy the hedge.

Code 
closing<-21884.9
strikerate <- 20000  # Strike price of the option
time<- 210/365  # Time to expiration in years
risk_free_rate <- 0.071   # Risk-free interest rate
vol<-vol # implied volatility

price<-EuropeanOption(type = "put",underlying = closing,strike = strikerate,dividendYield = 0,riskFreeRate = risk_free_rate,maturity = time,volatility = vol)
price
Concise summary of valuation for EuropeanOption 
     value      delta      gamma       vega      theta        rho     divRho 
  293.1177    -0.1638     0.0001  4100.4435  -403.4529 -2230.1221  2061.5794
Code 
strikerate
[1] 20000

Monetising the hedge

§a passive - at the time of expiry.

§b Empirical multiples of Initial cost. 

§a is ideal for long time horizon with potential big drawdown happening once or twice. §b out performs §a if no such tail events occur. In such a situation, even no-hedge strategy performs better than one with a hedge. 

For the hedging to outperform a pure buy and hold strategy with out hedging, it should be monitised at 8- 10 times the initial premium or a catastrophy should happen. In any case, the proceedings should be used to buy further far OTM puts and rest may be invested in the crashing asset.

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