How to determine Black-Scholes current Rate number?

W

Wait4proof

I've always had a hard time making "reliable" Option Pricing calculations. I would like to think that since the Black-Scholes formula is math, that the solution would be math also. But the more time goes by, the more I am convinced that the formula is voodo instead.

Sure, I understand IV is going to bounce around unpredictability, but lately it seems that the Rate number is doing the same crazy bounce. Is anyone else noticing this?

So my question is, is there a mathematical way to pin-down the Rate?
Or, is there at least a guaranteed way to look-up the Rate somewhere?

Thanks.
 
Atticus,

For option valuation, I believe a risk-free rate (US treasury rate for valuating options in the US) should be used instead of LIBOR. Also, ideally the maturity of the risk-free rate should match the maturity of the option.

As to valuating options with changing risk-free rate, I believe one can use Monte-Carlo simulation to do the work.




Quote from atticus:

I doubt your size is sufficient to warrant using anything but a LIBOR figure matched to the duration. Not meaning it as an insult. http://www.bloomberg.com/quote/US0003M:IND
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Quote from JefeTrader:

Atticus,

For option valuation, I believe a risk-free rate (US treasury rate for valuating options in the US) should be used instead of LIBOR. Also, ideally the maturity of the risk-free rate should match the maturity of the option.

As to valuating options with changing risk-free rate, I believe one can use Monte-Carlo simulation to do the work.
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Actually you should use your own funding rate because that is the cost it is for you to replicate the option.

But unless you are trading 7 year options, running levered boxes, or trading deep deep in the money options, it is a minor driver of PNL.

When I was trading vol institutionally, only once was rho a driver of my pnl. And it was a multi billion dollar dividend trade where eonia rates were much much higher than 3M libor rates in 07/08. Even then the pnl was 20bps on notinoal.
 
Quote from newwurldmn:

Actually you should use your own funding rate because that is the cost it is for you to replicate the option.

But unless you are trading 7 year options, running levered boxes, or trading deep deep in the money options, it is a minor driver of PNL.

When I was trading vol institutionally, only once was rho a driver of my pnl. And it was a multi billion dollar dividend trade where eonia rates were much much higher than 3M libor rates in 07/08. Even then the pnl was 20bps on notinoal.
More...

Well sure, but for modeling O/U on a sheet. I am funding at 15 points if I am netting with Joe the bookie.
 
Here's a bit more about my problem: after plugging-in all the numbers into Black-Scholes (including the IV number that I get from TDA), I adjust the Rate number until the BS Option price matches the real middle of Bid/Ask. And I am seeing numbers like -0.4 and -0.02 rate. This just seems screwed-up.

Now, 2 of you are saying "matched to the duration" and "match the maturity of the option", but I always trade 2-5 week expiration. So how can I do that?

I'll post my BS code just in case too:
Code: 
function BlackScholes(isCall, stockP, strike, expT, impV, rate){
	var d1,d2,optprice, sigT=impV*Math.sqrt(expT);
	d1=( Math.log(stockP/strike) + ( (rate+((impV*impV)/2)) *expT) )/sigT;
	d2=d1-sigT;
	if(isCall){
		optprice = (stockP * NormCDF(d1)) - (strike * Math.exp(-rate*expT) * NormCDF(d2));
	}else{
		optprice = (strike * Math.exp(-rate*expT) * NormCDF(-d2)) - (stockP * NormCDF(-d1));
	}
	return optprice;
}
function NormCDF(z){// cumulative density of normal (excel NORMSDIST)
	if(z>6.0)return 1.0; if(z<-6.0)return 0.0;// guard against overflow
	var p=0.2316419, b1=0.31938153, b2=-0.356563782, b3=1.781477937, b4=-1.821255978, b5=1.330274429;
	var a,t,norm,cdf, c2=0.3989423;// = (1.0/sqrt(2*Math.PI))
	a=Math.abs(z);
	t=1.0/(1.0+(a*p));
	norm = c2 * Math.exp((-z)*(z/2.0));//normal distribution
	cdf = (b1+((b2+((b3+((b4+(b5*t))*t))*t))*t))*t;
	cdf = 1.0-(norm*cdf);
	if(z<0.0) cdf=1.0-cdf;
	return cdf;
}
 
Quote from Look4aSine:

after plugging-in all the numbers into Black-Scholes (including the IV number that I get from TDA), I adjust the Rate number until the BS Option price matches the real middle of Bid/Ask. And I am seeing numbers like -0.4 and -0.02 rate. This just seems screwed-up.
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Hard to know without seeing your dataset -- can you post it? -- but possibly some combination of: imprecise IV, overlooked dividends, or not accounting for hard-to-borrows. The numbers you get for 'rate' are zero'ish, as they should be. It's very likely you're on a fool's errand.
 
Quote from Look4aSine:

...... But the more time goes by, the more I am convinced that the formula is voodo instead......
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Now your getting the idea!!
 
Quote from Look4aSine:

Here's a bit more about my problem: after plugging-in all the numbers into Black-Scholes (including the IV number that I get from TDA), I adjust the Rate number until the BS Option price matches the real middle of Bid/Ask. And I am seeing numbers like -0.4 and -0.02 rate. This just seems screwed-up.

Now, 2 of you are saying "matched to the duration" and "match the maturity of the option", but I always trade 2-5 week expiration. So how can I do that?

I'll post my BS code just in case too:
Code: 
function BlackScholes(isCall, stockP, strike, expT, impV, rate){
	var d1,d2,optprice, sigT=impV*Math.sqrt(expT);
	d1=( Math.log(stockP/strike) + ( (rate+((impV*impV)/2)) *expT) )/sigT;
	d2=d1-sigT;
	if(isCall){
		optprice = (stockP * NormCDF(d1)) - (strike * Math.exp(-rate*expT) * NormCDF(d2));
	}else{
		optprice = (strike * Math.exp(-rate*expT) * NormCDF(-d2)) - (stockP * NormCDF(-d1));
	}
	return optprice;
}
function NormCDF(z){// cumulative density of normal (excel NORMSDIST)
	if(z>6.0)return 1.0; if(z<-6.0)return 0.0;// guard against overflow
	var p=0.2316419, b1=0.31938153, b2=-0.356563782, b3=1.781477937, b4=-1.821255978, b5=1.330274429;
	var a,t,norm,cdf, c2=0.3989423;// = (1.0/sqrt(2*Math.PI))
	a=Math.abs(z);
	t=1.0/(1.0+(a*p));
	norm = c2 * Math.exp((-z)*(z/2.0));//normal distribution
	cdf = (b1+((b2+((b3+((b4+(b5*t))*t))*t))*t))*t;
	cdf = 1.0-(norm*cdf);
	if(z<0.0) cdf=1.0-cdf;
	return cdf;
}
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You "rate" here is a combination of dividends, borrow rate and the actual interest rate. That's why you are getting negative rates.
 
Oh boy, here we go, "overlooked dividends, or not accounting for hard-to-borrows" and again, "combination of dividends, borrow rate and the actual interest rate" - what a nightmare. I'm not sure if I even want to figure out what you both are talking about.

How about this instead:
I want to calculate potential profit, how can I semi-reliably do this using the BS formula?

For instance, can I "assume" these steps will work:
1) Enter the current numbers (stock, strike, exp, IV)
2) Adjust the Rate until I match the current/market Option price
3) Use that Rate for the duration of the option to calculate step 4-6
4) Plug-in a projected Stock price
5) Subtract the number of days I hope that the stock movement to occur in
6) Click "Calculate" to see what the Option price will be at on that day

These are the step I use now, and like I said, it seems like voodoo.

Anyone care to tell me how they personally do it, step by step?
Thanks again for the help and insights.
 
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