s**7
发帖数: 4 | 1 For options, GARCH is one of the method used to model historical volatility.
Does anybody know which method is used to model volatility for commodity
future? |
w*********r
发帖数: 488 | 2 GARCH不是model option的volatility，是model underlying asset of option，而且
不仅局限于此，股票的收益，inflation rate，exchange rate都可以用GARCH来
forecast他们的volatility。我觉得future作为衍生品和我上面说的东西是不一样的，
因为它的价格是通过no arbitrage pricing定出来的，future 的价格应该不是一个
random walk。
volatility.
【在 s**7 的大作中提到】
: For options, GARCH is one of the method used to model historical volatility.
: Does anybody know which method is used to model volatility for commodity
: future?
|
s**7
发帖数: 4 | 3 Future is the derivative of underlying asset price.
For commodity, asset price is spot price.
Black-schole's stock price is assumed to be random walk.
I figure spot price should be random walk too.
option price is derived based on 'no arbitrage' too. Future price is just
not calculated from stochastic PDE. But I am sure future price, same as
option price, must have volatility.
right?
【在 w*********r 的大作中提到】
: GARCH不是model option的volatility，是model underlying asset of option，而且
: 不仅局限于此，股票的收益，inflation rate，exchange rate都可以用GARCH来
: forecast他们的volatility。我觉得future作为衍生品和我上面说的东西是不一样的，
: 因为它的价格是通过no arbitrage pricing定出来的，future 的价格应该不是一个
: random walk。
:
: volatility.
|
C*A
发帖数: 63 | 4 future price = spot price + carry cost
since carry cost is small, future price still follows random walk if you
assume the underlying security exhibits random walk. |
w*********r
发帖数: 488 | 5 我的意思是说，future的价格不是自己随便乱动的，一旦知道它的underlying asset的
价格，future的价格就是certain的了，就不存在uncertainty了。如果定义S0为
underlying asset的spot price，F0为当期该资产future的价格，该future在T时到期
，riskfree interest rate为r的话，F0必然为，F0=S0*exp（r*T）（最简单的情形，
该资产在到期日之前不产生income，保管该资产没有cost，等等）。
可是股票的价格不是这样的，给你什么已知条件，你也算不出来股票的价格一定是多少
啊，这就是衍生品和非衍生品的区别。我的意思说衍生品是没有variance，没有
volatility的，所有说衍生品的volatility，都是指它的underlying asset的
volatility。
【在 s**7 的大作中提到】
: Future is the derivative of underlying asset price.
: For commodity, asset price is spot price.
: Black-schole's stock price is assumed to be random walk.
: I figure spot price should be random walk too.
: option price is derived based on 'no arbitrage' too. Future price is just
: not calculated from stochastic PDE. But I am sure future price, same as
: option price, must have volatility.
: right?
|
s**7
发帖数: 4 | 6 When I check Black-scholes option pricing model,
The price of the underlying instrument St follows a geometric Brownian
motion with constant drift μ and volatility σ:
Yes. volatility σ refers to unerlying asset's volatility.
Also check here: http://en.wikipedia.org/wiki/Implied_volatility#Solving_the_inverse_pricing_model_function
the implied volatility of an option contract is the volatility implied by
the market price of the option based on an option pricing model.
////About historical volatil |
