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Alkmene
Topic Author
Posts: 301
Joined: January 18th, 2007, 10:19 pm

### Futures and Expectation

I do understand the following: A Forward rate is an expectation of the future sport rate under the forward measure.I do not understand what it means that a Futures, because it is settled every day, is a "simple" expectation of a spot rate in the future.I can see the reasoning in the second statement but if implied rates from Futures are generally too high due to convexity considerations, why would they be a true (if "simple" means real world expectation); they would be, at times, ridiculously high?Thanks,Alk

eh
Posts: 494
Joined: March 2nd, 2010, 9:26 am

### Futures and Expectation

Where did you read that? I don't think that "simple" means "real world".

animeshsaxena
Posts: 520
Joined: June 19th, 2008, 2:56 pm

### Futures and Expectation

It's a risk neutral measure not real world measure. If you take expectation with real measure then you will get forward price as S0 exp(mu + sigma^2/2) which is wrong coz it doesn't agree with arbitrage price. Simple arbitrage pricing shows it should be S0 e^(rT). In risk neutral measure you get the arbitrage price of the expectation you compute.

ronm
Posts: 163
Joined: June 8th, 2007, 9:00 am

### Futures and Expectation

Hi animeshsaxena, isn't the expectation would be simply S0 exp(mu * t) only if I assume GBS as diffusion equation for spot?
Last edited by ronm on April 27th, 2011, 10:00 pm, edited 1 time in total.

Alkmene
Topic Author
Posts: 301
Joined: January 18th, 2007, 10:19 pm

### Futures and Expectation

QuoteOriginally posted by: ronmHi animeshsaxena, isn't the expectation would be simply S0 exp(mu * t) only if I assume GBS as diffusion equation for spot?No, because it is lognormal and the mean of a lognormal is e^(E(normal)+sigma^2/2))Alk

Alkmene
Topic Author
Posts: 301
Joined: January 18th, 2007, 10:19 pm

### Futures and Expectation

QuoteOriginally posted by: ehWhere did you read that? I don't think that "simple" means "real world".A paper where I lost the first page; I think it is a poorly worded para. What they meant was that there is no need to discount to get a PV because it is settled daily.Thanks,Alk

ronm
Posts: 163
Joined: June 8th, 2007, 9:00 am

### Futures and Expectation

QuoteOriginally posted by: AlkmeneQuoteOriginally posted by: ronmHi animeshsaxena, isn't the expectation would be simply S0 exp(mu * t) only if I assume GBS as diffusion equation for spot?No, because it is lognormal and the mean of a lognormal is e^(E(normal)+sigma^2/2))AlkBut in the expectation part of log(ST), sigma is involved, isnt it? logST ~ N(logS0 + (mu - 0.5*sigma^2)*T, sigma*sqrt(T))Thanks,

ronm
Posts: 163
Joined: June 8th, 2007, 9:00 am

### Futures and Expectation

This trash thing is pinching me quite a bit...............can somebody please clarify, have I done any mistake there? Thanks,

list
Posts: 2041
Joined: October 26th, 2005, 2:08 pm

### Futures and Expectation

From http://www.riskglossary.com/link/EMM.htmIt is a standard assumption of economics that markets are arbitrage free. If we make that assumption, the fundamental theorem of asset pricing tells us there is an equivalent martingale measure , and we can use to calculate asset prices as expectations. More often than not, this is how financial engineers approach option pricing or other financial engineering problems today.Fundamental Theorem of Asset Pricing applied for the forward contracts written on different assets which price is governed by GBMs with expected return from ( - infinity , + infinity ) and equal volatility say 0.1 should be priced equally. That is a practical trash statement which follows from the wrong assumption that spot price is expected value of something. We need to discount payoffs by risk free ir. In order to avoid arbitrage we need to replace real rate of return on risk free. The people who invented this pricing did not correctly interpreted "price" as well as did not correctly interpreted Girsanov measure change technique.