Arbitrage -Understanding Put – Call Parity

Dharam Chand Sethia Uncategorized Leave a Comment

Arbitrage is defined as Risk Free profit.

There are 2 ways of it.

  • When there are 2 portfolios, having same payoff; but different costs ,then there’s an arbitrage.
  • When Investment returns(Fixed) are greater than Borrowing costs.

Example – Arbitrage between 2 markets on same securities.Put Call Parity,Interest Rate Parity.

An exchange would always want a Arbitrage Free pricing with Good liquidity, but it’s tough in initial days of any exchange(BSE derivatives) or a new product(india VIX derivatives) unless it is an extension of existing product(weekly options on banknifty was an extension).

Theory Vs Practical.

In theory arbitrage is just a formula/mathematical equation where if Right Hand Side ≠ Left Hand Side then there is an Arbitrage and Profit making potential.

In Practice, Markets are more than just a Mathematical equation.There are Taxes,Regulatory challenges,Transaction  costs, Opportunity costs that prohibits one to operate arbitrage in Markets.Different Markets have different practices.For example in Indian markets one cannot short sell equities overnight, margin structure in derivatives segment has very big opportunity & transaction costs. With all these factors arbitrage just remains a fancy word in theory,which is good and healthy for liquid markets.

In this post i will give you a detailed example of PUT CALL parity.

In options market arbitrage free pricing is achieved with put call parity.

Put Call Parity defines the relationship of the Call and Put of same underlying,strike and expiry.If i buy a European Call option and Short a European Put option then i will get the same payoff as the long forward/futures contract.

Call Option Premium + Present Value of Strike Price = Put Option Premium + Spot Price



In Indian markets we modify this a bit for practical purposes/usage.The formula goes like this-

P(put)+F(futures) = C(Call)+S(Strike).

This above formula is a modified version of the original one and used for smooth execution.

Usage & Benefits:

  • Proper Pricing of illiquid pair of strikes(CALL OR PUT).
  • Creating Synthetic Products using Futures.
  • Equation is independent of time and volatility, makes it robust.




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