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outrun
Posts: 4573
Joined: April 29th, 2016, 1:40 pm

### Re: to Black Scholes pricing

In the binomial model you don't care about mu: if the stock goes up or down ..your P&L of the hedged call is in both cases zero.

This means that the probability of going up -and hence the value of mu- does not matter if you hedge!

list1
Topic Author
Posts: 1696
Joined: July 22nd, 2015, 2:12 pm

### Re: to Black Scholes pricing

In the binomial model you don't care about mu: if the stock goes up or down ..your P&L of the hedged call is in both cases zero.

This means that the probability of going up -and hence the value of mu- does not matter if you hedge!
outrun, You right. In BS scheme distributions S up-down are given with the help of explicit parameters (mu, sigma). In binomial scheme distributions up-down are  given directly and all constructions are given with the help of $S_{down} ,p_{down} ; S_{up} , p_{up}$ . Though I think one can try to present value mu and express hedging ration in terms of mu. Though no one need that.

list1
Topic Author
Posts: 1696
Joined: July 22nd, 2015, 2:12 pm

### Re: to Black Scholes pricing

I submitted a paper to

https://papers.ssrn.com/sol3/papers.cfm ... id=3056738

list1
Topic Author
Posts: 1696
Joined: July 22nd, 2015, 2:12 pm

### Re: to Black Scholes pricing

I submitted a paper to

https://papers.ssrn.com/sol3/papers.cfm ... id=3056738
In this paper
1. informal differential form of the BSE derivation is replaced by its formal integral form
2. it is shown that hedging on a finite time interval represents a pricing problem that does not effect BS pricing
3 it is highlighted the difference between no arbitrage and settlement pricing of the options
and something else.

frolloos
Posts: 1621
Joined: September 27th, 2007, 5:29 pm
Location: Netherlands

### Re: to Black Scholes pricing

3 it is highlighted the difference between no arbitrage and settlement pricing of the options
and something else.
This ("and something else") is a classic
Last edited by frolloos on October 23rd, 2017, 5:05 pm, edited 1 time in total.

list1
Topic Author
Posts: 1696
Joined: July 22nd, 2015, 2:12 pm

### Re: to Black Scholes pricing

3 it is highlighted the difference between no arbitrage and settlement pricing of the options
and something else.
This ("and something else") is a classic
Something is related to my point on options pricing, which interprets premium as settlement between buyers and sellers and therefore implies market risk of the premium. Nonstochastic BS premium is implied by oversimplified problem setting that follows from no arbitrage framework of the pricing problem. It will be o'k if we had sufficient conditions that convince us that buyers and sellers always follow the pricing rule which is directed by BS hedged portfolio.
In particular, when we interpret price as a solution of equality of EPVs of two cash flows buyer and seller  like irs we interpret price as an estimate of settlement price. It looks much better for me than interpret swap price like a portfolio options in BS world.

Paul
Posts: 11267
Joined: July 20th, 2001, 3:28 pm

### Re: to Black Scholes pricing

3 it is highlighted the difference between no arbitrage and settlement pricing of the options
and something else.
This ("and something else") is a classic
Para subir al cielo,
Para subir al cielo se necesita,
Una escalara grande,
Una escelara grande y otra chiquita

frolloos
Posts: 1621
Joined: September 27th, 2007, 5:29 pm
Location: Netherlands

### Re: to Black Scholes pricing

A BS hedging ladder

list1
Topic Author
Posts: 1696
Joined: July 22nd, 2015, 2:12 pm

### Re: to Black Scholes pricing

3 it is highlighted the difference between no arbitrage and settlement pricing of the options
and something else.
This ("and something else") is a classic
Para subir al cielo,
Para subir al cielo se necesita,
Una escalara grande,
Una escelara grande y otra chiquita