risk-free rate

S

stevenpaul

Dear Gentlemen (and ladies, if there are any--god forbid),

The risk-free rate is one of the variables required in order to solve for the Greeks. It should be continuously compounded, as well (at least in the BSM model). Where can we get that data? Is there a site that lists the rate we should be using in our options equations down to two decimal places or so?

Thank you ever so much, as always!
 
Normally, as far as I am aware, people use the LIBOR curve to imply the risk-free rate, simply because it's the benchmark of sorts and is the most liquid. There are relatively easy, well-understood ways to construct these curves.

However, there's a LOT of rather deep issues arnd the choice of discounting, so it's not an obvious choice. My understanding is that, most recently, more and more people are switching to using OIS rates. Moreover, there's a valid argument that, in order to achieve self-consistency and avoid arbitrage, one should always use one's own specific funding rate, whatever it might be.

Anyways, maybe it's just me waxing poetic about discounting, 'cause it's a subject so very near and dear to my heart. Maybe actual equity/index options (I assume your question is about those) practitioners would comment and say that they just don't give a damn.
 
Quote from stevenpaul:

Is there a site that lists the rate we should be using in our options equations down to two decimal places or so?
More...

ivolatility basic calculator gives the i rates used in their calcs. I don't know if those are the rates that you should be using.
 
The risk free rate is a concept beloved of micro-economists and bond math geeks. It's the building block of Modern Portfolio Theory and an input into option pricing models. It's supposed to represent the interest rate available in the market that is without credit risk and as such is the lowest interest rate in the market. The complete absence of risk has always been more observable in theory than in practice but in the last month or so, swap rates have fallen below gilt yields - can it be right that the lowest interest rate in the market is lower than the traditional risk free rate? Are government bonds still the right instrument with which to observe the risk free rate?

Interest rate swaps are a means of turning a floating rate cashflow into a fixed rate cashflow for a set period of time, or vice versa. If you decided to receive fixed rate payments for ten years, you would agree to pay Libor (reflecting the cost of short term money) and receive the fixed payment for the life of the contract from the bank with which you'd traded. Historically the fixed rate payment would be more than you could get by buying a gilt from Her Majesty's government. On average over the past decade it was around 0.5% more than the ten year gilt yield. This seems to make sense, as there is a risk that the bank counterparty that you have traded with disappears and can no longer service the contract, so the premium over gilts reflected credit risk.


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http://www.bondvigilantes.co.uk/blog/2010/02/25/1267087560000.html

Quite interesting read... :cool:
 
Quote from Martinghoul:

Normally, as far as I am aware, people use the LIBOR curve to imply the risk-free rate, simply because it's the benchmark of sorts and is the most liquid. There are relatively easy, well-understood ways to construct these curves.

However, there's a LOT of rather deep issues arnd the choice of discounting, so it's not an obvious choice. My understanding is that, most recently, more and more people are switching to using OIS rates. Moreover, there's a valid argument that, in order to achieve self-consistency and avoid arbitrage, one should always use one's own specific funding rate, whatever it might be.

Anyways, maybe it's just me waxing poetic about discounting, 'cause it's a subject so very near and dear to my heart. Maybe actual equity/index options (I assume your question is about those) practitioners would comment and say that they just don't give a damn.
More...

np?
 
I just use the two year USG bond yield. While it's an input to my probability model, it's not terribly important. Rho is the greek for this, and I don't think anyone really sweats much over it.
Which will, one day, turn out to be a mistake, I'm sure...
 
Quote from Blotto:

Your risk free rate.
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I've seen this answer many times.

Option pricing is based on certain assumptions that don't apply to retail traders. We all have our own cost of carry. It's not practical to apply it in most situations for the average retail.
 
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