Hedge pricing

Calculate implied volatility

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

Warning: ^NSEI contains missing values. Some functions will not work if objects
contain missing values in the middle of the series. Consider using na.omit(),
na.approx(), na.fill(), etc to remove or replace them.

Get closing price

# Extract the last closing price directly from nifty_data
closing_price <- nifty_data[.N, close]
closing_price

[1] 25966.4

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.

library(quantmod)
library(RQuantLib)

# Define option parameters for a single observation
nifty_price<-25966.4
option_price <- 85  # Current market price of the option
strike_price <- 25966.4*.8  # Strike price of the option
time_to_expiry <- 365/365  # 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] 0.1794754
attr(,"class")
[1] "EuropeanOptionImpliedVolatility" "ImpliedVolatility"              

At present the implied volatility is 18

Option pricing calculation

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

closing_price<-25966
strike <- 25966 * 0.85  # Strike price of the option
time_to_expiry <- 365/365  # 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:

print(closing_price)

[1] 25966

cat("Strike price:\n")

Strike price:

strike

[1] 22071.1

price

Concise summary of valuation for EuropeanOption 
     value      delta      gamma       vega      theta        rho     divRho 
  187.8179    -0.0821     0.0000  3937.7416  -188.6070 -2320.5182  2132.7003 

Price of a 12 month 8 delta option is 188 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.

closing<-25966
strikerate <- 21000  # Strike price of the option
time<- 365/365  # 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 
   98.6349    -0.0477     0.0000  2577.1354  -136.4082 -1336.0278  1237.3930 

strikerate

[1] 21000

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.