@Ju1882 21 August 2020

Put-call Parity Theory.

****Background**** Put-call parity is an important principle in options pricing first identified by Hans Stoll in his paper, The Relation Between Put and Call Prices, in 1969. Put-call Parity Theory is based on theory of one price. As per this theory of one price, if two assets are expected to have same value on a future date, they should have same cost today. ****Example**** Suppose we have two portfolios. (1) Buy 1 BTC for $9,000, also buy European put ( Expiry date - 1 year ) of 1 BTC at a strike price of $10,500. (2) Buy 1 European call ( Expiry date - 1 year ) at a strike price of $10,500 and 1 Bond carrying Risk free return. ( The amount to be invested in Bond should be such that on the date the Call expires, the bond value including interest should be equal to the strike price ). **On maturity** **Case I :-** Spot price of BTC is $ 10,000. ( Less than strike price ). Value of Portfolio (1) = Value of put on maturity + Spot price = (10,500-10,000) + 10,000 = $10,500 Value of Portfolio (2) = Value of call + Maturity amount of Bond = 0 + 10,500 = $10,500 **Case II :-** Spot price of BTC is $11,000 ( Higher than strike price ). Value of Portfolio (1) = Value of put on maturity + Spot price = 0 + 11,000 = $11,000 Value of Portfolio (2) = Value of call + Maturity amount of Bond = ( 11,000-10,500 ) + 10,500 = $11,000 **Case III :-** Spot price of BTC is $10,500 ( Equal to the strike price ). Value of Portfolio (1) = Value of put on maturity + Spot price = 0 + 10,500 = $10,500 Value of Portfolio (2) = Value of call + Maturity amount of Bond = 0 + 10,500 = $10,500 **Both portfolios will have same value on maturity whether the spot price is less than or equal to or greater than the strike price.** **Hence, both the portfolios should have same cost today (Put-call Parity Theory).** **Cost of portfolio (1)** = Spot price + Put premium **Cost of portfolio (2)** = Call premium + Value of Bond = Call premium + Present Value of Bond Hence, combining (1) and (2) ****Conclusion**** **Spot price + put premium = Call premium + Present Value of Bond** Thank you for reading. Cricket Lovers are invited to join. Cricket Community :- Cricket Lovers (be22) Link :- https://read.cash/c/cricket-lovers-be22