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darkvader
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Joined: November 14th, 2019, 4:40 pm

Discrete Form of Ho Lee

November 14th, 2019, 4:43 pm

Can someone help with the discrete form of a Time Varying Drift with Constant Volatility asset price equation?
Additionally, any suggestions on applying time varying drift framework to Trend systems?
 
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Alan
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Re: Discrete Form of Ho Lee

November 16th, 2019, 7:33 pm

Pretty vague. Starting from here, a discrete form might be:

[$]r_t = r_{t-1} + \theta_t + \epsilon_t[$], where [$]\epsilon_t \sim N(0,\sigma^2)[$], where '[$]\sim[$]' means "is distributed as". 

N(0,v) denotes an (independent) normal distribution at each step with mean-0 and variance [$]v[$]. Finally, [$]\theta_t[$] is simply some deterministic sequence. 

As far as your application, hard to say, other than to learn how to apply maximum likelihood to your data. There are a zillion books on time series modelling.
 
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bearish
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Joined: February 3rd, 2011, 2:19 pm

Re: Discrete Form of Ho Lee

November 16th, 2019, 7:56 pm

I was going to reply, but got confused by the title. The Ho-Lee model, as published in the JF in 1986 was discrete to begin with. Some of us thought it an important paper at the time, and for at least a few years thereafter, since it essentially ushered in the HJM style of modeling future term structure dynamics as a separate exercise from explaining the current yield curve. This was very useful from the perspective of managing an interest rate derivatives book. And, admittedly, almost completely useless from the perspective of managing a bond portfolio. I'm rather in the dark as to whatever Mr Vader is looking for...