# Tag Info

### Risk-free: why LIBOR pre-crisis and OIS now

It comes down to the definition of LIBOR: London Interbank Offer Rate -> Every business day, a panel of large banks are asked by the BBA[*] (British Bankers Association) at what rate they would lend ...
• 507

### Why do we discount in ois and not treasuries

There are two parts to this question: 1) Is OIS a good risk-free proxy? and 2) Why is OIS used to discount cash flows of derivatives. First, overnight indexed swaps, in the US, are indexed to the Fed ...
• 11.7k
Accepted

### Drift rate vs. Riskless rate in the Black-Scholes model

Let's take your questions in turn - If volatility isn't a concern, an investor is concerned with $$E[\log S_T] = \log S_0 + (\mu - \tfrac{1}{2}\sigma^2)T$$ when deciding to purchase a stock, ...
• 5,911

### Drift rate vs. Riskless rate in the Black-Scholes model

Perhaps some big picture background is useful. The Black-Scholes formula was originally developed through a dynamic hedging argument, that by trading a stock and a riskless bond in continuous time, ...
• 6,944
Accepted

### Is there any public data to get OIS for differal time (1d, 1W, 1M, ..., 10Y)?

So you can get depo and swap rates from markit daily, at links like this: http://www.markit.com/news/InterestRates_<cncy>_<yyyymmdd>.zip i.e. http://...
• 2,571
Accepted

### Overnight Index Swaps (OIS) vs. Fed Funds Futures

I think you have a little misunderstanding. OIS just means the rate for fed funds. Usually people are referring to "FEDL01 Index" on Bloomberg. That's the VWAP of trades for the previous day in Fed ...
• 2,613
Accepted

### What is the distribution of the risk-free asset?

The standard way to think about this is that at time $t$ the riskless asset gives you known return of $r_{f,t}$ over a short time period. However, this rate may itself be time-varying and stochastic ...
• 1,727

### Which proxy is the best to calculate daily risk free rate for a capital asset pricing model?

There are many proxies for the risk free interest rate. For most purposes you may need a short term risk free rate, but there are in general no significant differences which one you chose. Treasury ...
• 2,916

### What is the risk-free rate of a precious metal, e.g. gold?

The current price of future access to any asset is its current forward price. This is true for any asset and true for whatever currency you use to measure price. Once you have the forward prices it is ...
• 2,003

### how to calculate daily risk free rate using 13 week treasury bill

user233051 notes that ^IRX is indeed the official discount rate of the US Treasury. So to answer his question we need to exactly understand how the Treasury computes the discount rate. My answer is ...

### Calculating the Risk Free Rate

Hint: If these 2 stocks have perfect negative correlation (correlation: -1), then you can construct a risk free portfolio. What would the return on that risk free portfolio be?
• 6,532
Accepted

### Sharpe Ratio, risk free rate

No, this is not the same. For example, consider the scenario \begin{align*} r_A &= 10\% \quad\quad \sigma_A = 10\% \\ r_B &= 1.5\% \quad\quad \sigma_B = 1\% \\ \end{align*} If $r_f=1\%$, ...
• 741
Accepted

### Why use the risk-free rate for discounting in a risk neutral world?

The first statement is kind of clear. If all investors are risk-neutral, they simply do not care about risk and do not pay more or less regardless how risky an asset is. As a consequence, the return ...
• 15.9k
Accepted

### Proof that we can price any derivative as the discounted value of its expected return under the risk neutral measure

This holds due to a change of measure. There is the real-world $\mathbb{P}$ and the risk-neutral world $\mathbb{Q}$. (I am going to assume constant interest rate $r$) The first fundamental theorem of ...
• 15.9k

### Overnight Index Swaps (OIS) vs. Fed Funds Futures

All above is correct. Just adding my 2 cents as the former PM for WIRP... These days Bloomberg's WIRP uses both Fed Funds Futures (US-Fut) and OIS (US-OIS) to back out the interest rate expected after ...
Accepted

### What is the standard risk free rate used to discount options?

Since pretty much all trades (at least interbank) are collateralized nowadays, you would follow the principle of CSA discounting and use the interest rate on the collateral as a discount rate. ...
• 56

### What is the distribution of the risk-free asset?

Just to add to the previous answer, one example of such asset (returning 'risk-free rate') is a money market (or bank) account, but it is only locally risk-free, with value accruing continuously at ...
• 5,043
Accepted

### Why must the risk free rate be free from risk in risk neutral valuation?

A non academic answer: In the real world, when dealers or professional counterparties trade options with each other, the option premium is not funded by the dealer's unsecured borrowing. Rather, ...
• 17.1k

### What is the risk-free asset?

Well, I do not think there is a large difference: Given you deposit money at a Bank the value of this deposit changes according to $$\frac{dB_t}{B_t} = r dt$$ which simply means there is no ...
• 1,456
Accepted

### Valuing derivatives under stochastic interest rates

A few points can be noted. The CIR model is usually for a short, or instantaneous, spot rate $r_t$, which is the forward rate over an infinitesimal interval. That is, \begin{align*} r_t = \lim_{\...
• 21.1k

### Calculate excess returns for Sharpe Ratio with today's or past risk free rate of return?

You can refer to Sharpe's paper. If you are computing an ex post Sharpe Ratio, you should calculate the excess return for each period as the return of the fund over the risk free rate return over that ...
• 955

### Why is a risk-free portfolio desirable?

You are absolutely right that no one would like to replicate return of risk free assets when such instrument is easily available in the market and can be bought directly. So, why financial managers ...
• 2,238

### Which risk free rate is assumed by market when pricing american options?

The risk-free rate used in the valuation of options must be the rate at which banks fund the cash needed to create a dynamic hedging portfolio that will replicate the final payoff at expiry. Dealers ...
• 2,147

### How does a Delta Hedged portfolio yield the Risk-free?

I'll put here the answer provided in a comment by @dm63 (thanks by the way): The requirement that the portfolio earns the risk free rate is something we are imposing in order to calculate the ...

### Is EONIA swap rate really credit risk free?

It’s not entirely risk-free. Nothing in life is. The comet could hit etc. The difference is suppose I had a 100m OIS swap line open with Lehman, margined overnight. OIS settles at 1.81% vs 1.80%; and ...
• 5,061

### Which risk-free rate to use for the UK?

I would use SONIA. That's the official RFR for the UK. See this BoE link: https://www.bankofengland.co.uk/markets/transition-to-sterling-risk-free-rates-from-libor
• 2,252
Accepted

### Risk-free yield curve creation for Euro

For Bloomberg, there are technically two swap curves that could work: -ICVS 133 for EUR OIS and -ICVS 514 for €STR. I agree with ...
• 8,739

### How to determine risk-free rate of Ecuador?

Since Ecuador uses the US dollar, the appropriate rate to use for discounting is the US dollar risk-free rate (i.e. the zero coupon rate bootstrapped from the overnight swap curve). The US dollar is ...
• 5,911