Spot-futures pricing model (with time to maturity and volatility)

[John TRD]

I am looking for price model for spot and futures Maybe you can recommend something intresting? Price can include (time until expiration) and volatility in spot,price of spot What i should looking for?

Maybe books which can describe correlation between spot and futures?

Something like this paper "Time-Varying Spot and Futures Oil Prices Dynamics"
http://www.brunel.ac.uk/__data/assets/pdf_file/0015/82032/1006.pdf

HOW futures become equal to spot price.
http://www3.cs.stonybrook.edu/~skiena/691/2007/lectures/lecture3.pdf
F=S*EXP(r*T) where F -forwad price S price for basic(for example stock or commodities oil) T-time period
But i am looking for price model near time expiration(maturity of futures) wheref tures price almost equal to spot price and will be soon(after few hors,day) equal to spotprice)


http://www.investopedia.com/ask/answers/06/futuresconvergespot.asp
Why do futures' prices converge upon spot prices during the delivery month? (i need formula for this)




Relationship between the price volatility and the time- to-maturity of a futures contract Futures price

What i should read,what you can recommend for price models of futures and spot?(like Black Scholes but for spot-futures only) What quants use for modeling futures price Maybe some R packages?

 

[mhy]

I'm a noob at this, but let me try:

Assume
asset = S,
today = t
expiration of the futures contract = T

The futures price is the expectation at time t of the asset price at time T given today's asset price S(t)

That is, Fut(S, t, T) = E[S(T) | t, S(t)]
Now once you reach the delivery time, t will be equal to T and you just have E[S(T)] which you already know now, so it ceases to become random and you have Fut(S, T, T) = S(T) which is the spot price at expiry.

I believe the way you calculate Fut(S, T-delta, T) where delta is very small depends on the nature of the instrument and there may or may not be closed-form solutions to that.

 

[John TRD]

Fut(S, T, T) = S(T) which is the spot price at expiry.
I believe the way you calculate Fut(S, T-delta, T) where delta is very small depends on the nature of the instrument and there may or may not be closed-form solutions to that.

Hi thank you i already saw simillar formula
http://en.wikipedia.org/wiki/Forward_price
But i looking for price in the future (with volatility sigma,b and maybe brownian motion

 

[mhy]

But that formula is nothing but the underlying asset price S(t) assuming it follows GBM. Plugging that S(t) into the formula I wrote above would give you exactly the futures price.

What do you mean "price in the future"?

 

[diegosanaz]

You have a formula for F(t,T,St). If you want to assume that St follows a GBM, then by ito is easy to get a process for F. Therefore also a process for the spread, which should yield two results. Spread at T=0 and vol going to 0 when approaching maturity.

I think that is what mhy means

 

[John TRD]

IHi thanks, now i undestood it better