SERVING THE QUANTITATIVE FINANCE COMMUNITY

 
User avatar
billyx524
Topic Author
Posts: 45
Joined: February 12th, 2016, 4:48 pm

dumb question

January 22nd, 2020, 2:13 am

Hi,

This might be a dumb question but I find myself questioning a lot of things I either took for granted or overlooked in the past in recent days.

We know put call parity is obeyed in Black Scholes pricing model, but what is the condition/reason in the black scholes model that gurantees put call parity is obeyed.  I am thinking it is the no-arbitrage assumption that a riskless portfolio must earn the risk free rate.  Is this right?

Thanks
 
User avatar
bearish
Posts: 5688
Joined: February 3rd, 2011, 2:19 pm

Re: dumb question

January 22nd, 2020, 2:32 am

Yes, I think you are basically right. Put call parity is essentially model free, at least in terms of not relying on any assumptions about the underlying asset price dynamics. The canonical reference here is Merton's paper (Theory of rational option pricing). Buying a call and selling a put with the same strike price and expiry is tantamount to making a commitment to buying the asset at the strike price. That is very similar to a forward contract, with the possible exception that a standard forward contract is struck at a price that makes the initial value equal to zero. So, what can go wrong? I suppose counterparty performance risk. Or borrowing and lending rates being very different. Or shorting the underlying asset being impossible, or at least costly. But, given that the relevant trading strategies only call for establishing a position once and then closing it out at expiry, the supporting assumptions are not remotely as stringent as those underpinning the Black Scholes model.
 
User avatar
billyx524
Topic Author
Posts: 45
Joined: February 12th, 2016, 4:48 pm

Re: dumb question

January 22nd, 2020, 3:01 am

So is put call parity really obeyed in real financial markets?  I mean in C+ PV(X) = P + S, we need a risk free rate.  But the lending rate would be different for different market particpants.
ABOUT WILMOTT

PW by JB

Wilmott.com has been "Serving the Quantitative Finance Community" since 2001. Continued...


Twitter LinkedIn Instagram

JOBS BOARD

JOBS BOARD

Looking for a quant job, risk, algo trading,...? Browse jobs here...


GZIP: On