Simple Forward (Future) Contract Pricing Algo

[Jibber 10]

Greetings!

 

Let me start by saying this is my first post on this forum, so if I accidentally break any of the forum norms, please forgive me. I am a high school student interested in coding (one day) my own derivatives algos and I was hoping for some assistance. I have decided to start pretty simply buy coding a Forward Contract Pricing method. Here is what I have so far (this is done in a Java fork called Processing, but I think the general idea of what I'm trying to do can be read by anyone with coding experience):

 

// F0 = forward price
// S0 = the current price of the asset
// r = compounding risk free rate
// T = time to maturity

//F0 = S0 * e^(r*T)
//at the time T the customer will pay F0 (fixed at time t=0) to get the asset
//if F0 > S0 * e^(r*T), would by the asset and short forward contracts on that asset
//if F0 < S0 * e^(r*T), would sell the asset and enter a long forward contract on that asset

class ForwardPricing {
 double F0,S0,r,T; 

 ForwardPricing(double _S0, double _r, double _T) {
   F0 = 0.0;
   S0 = _S0;
   r = _r;
   T = _T;
 }

 double getValuation() {
   return ( Math.pow( Math.exp( 1.0 ),( r * T  ) ) );
 }

 double getPrice(double v) {
   return S0 * v ;
 }
}

 

I suppose my first question is what exactly would the compounding risk free rate be? I got that term from a website that gave me the formula for forward pricings (f0 = s0 * e^(r*T)) and as far as I can ascertain it is something along the lines of the interest rate of Tbills, or their Euro counterpart, and so on. And if that is an accurate definition (I'm open to others!), any advice on how I should compound them? There are some many terms in derivative related markets that I find myself getting confused frequently.

 

If anyone has any advice or constructive criticism, I would greatly appreciate it!

 

Thanks for your time,

 

Jibber

[Tradewinds 12]

A risk free rate will be a very small rate of return. The "market" is a Risk/Reward relationship. If you are willing to take more risk, you might get a bigger return, no guarantees. Currently Greece is paying 18% on their Bonds. Greece is considered high risk. I don't want to loan money to Greece, because I might never get my money back. What is going to motivate me to loan money to Greece? A higher rate of return.

 

Here is a link with some info about the risk-free rate:

 

Risk-Free Rate Of Return Definition

 

Investopedia states that, in practice, a risk-free rate does not exist. A risk-free rate would probably be comparable to what the banks are paying on a Certificate of Deposit. But I don't really know.

 

I know nothing about this calculation or derivatives. But I was imagining how you would use this calculation. Depending upon the output you need, and how you are going to use the information, that might determine the software that you should be using. For example, you might not need a programing language, a formula in a spreadsheet might work. Are you going to use the forward pricing calculation to scan through a list? Would it be used in a database? Is this for trading, or long term investing? How fast do you need the information? Do you have access to downloading the data you need? I'm not helping you with the calculation, but getting the right calculation is probably just a technicality.

 

Here is an interesting link:

 

Valuation of a Forward contract

[Tradewinds 12]

Here is the Wikipedia article:

 

Risk-free interest rate - Wikipedia, the free encyclopedia

 

It states that:

 

"Though a truly risk-free asset exists only in theory, in practice most professionals and academics use short-dated government bonds of the currency in question."

 

So I would look at the rate on the short term government bond as the starting point for the risk-free rate.

[Jibber 10]

Thanks for the reply. Yes, I have read that - that is where I got the 0.18 percent for my original code. (the 52-week coupon rate for US Tbills as of yesterday). The question is that some sources refer to the risk-free rate as being the compound risk-free rate. If it is just a question of re-evaluating the equation daily using the t-bill rate then thats no problem.....I'm trying to figure out if I need to feedback anything back into the equation. Thanks for your reply.

[Jibber 10]

As to why I am writing this software, it's not so much to actually use in the market - rather I want to understand derivatives from the ground up. So I'm writing implementations in c/c++/java

[SIUYA 11]

I am not 100% sure if this helps as it might be more a matter of definitions....while firms might differ on exactly what their individual risk free rate is - which makes a difference to what they might consider fair value.

Stick with the overnight cash rate from the government bonds.

It is naturally compounding every night if you deposit money with them and are credited the interest and you leave that interest in the account.

A good book to understand options from the ground up is by Sheldon Natenberg....for some light reading.