# All Questions

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9k views

### Earnings and valuation data sources online

Are there any free/cheap sources for historical data on company earnings and valuations? I can get historical price data from Google and Yahoo, and it looks like I can get about five years of ...
10k views

### Local Volatility vs. Stochastic Volatility

Are there any empirical observations or practices when to prefer Local Volatility Model for pricing over Stochastic Model or vice versa?
31k views

### Correlation between prices or returns?

If you are interested in determining whether there is a correlation between the Federal Reserve Balance Sheet and PPI, would you calculate the correlation between values (prices) or period-to-period ...
6k views

### Can the concept of entropy be applied to financial time series?

I am not familiar with the concept of entropy for time series. I am looking for good reference papers and examples of use.
85k views

I am preparing for the CFA level 2 exam, I got confused by the concept Z-spread and OAS. When a call option is added to a bond, since it is not favorable to the bond buyer, they would require more ...
2k views

### Market impact, why square root?

The standard method of market impact is the square-root formula $$\Delta P = c \cdot\sigma \cdot \sqrt{\frac{n}{\nu}}$$ where $\Delta P$ is the price change from executing ...
9k views

### Baye's rule for conditional expectations (Proof review)

The Baye's rule for conditional expectations states $$E^Q[X|\mathcal{F}]E^P[f|\mathcal{F}]=E^P[Xf|\mathcal{F}]$$ With $f=dQ/dP$ - thus being the Radon-Nikodyn derivative and $X$ being ...
19k views

### Formula for forward price of bond

What is the formula for the forward price of a bond (assuming there are coupons in the interim period, and that the deal is collateralised) Please also prove it with an arbitrage cashflow scenario ...
6k views

Using total return calculations is critical in developing security selection models. The standard way to measure total return is to develop a series of price-adjusted data. Investopedia describes the ...
20k views

### Should I use an arithmetic or a geometric calculation for the Sharpe Ratio?

What are the advantages/disadvantages of using the arithmetic Sharpe Ratio vs the geometric Sharpe Ratio? Is one more correct? Or is one better in certain circumstances?
9k views

### Should Sharpe ratio be computed using log returns or relative returns?

I am trying to reconcile some research with some published values of 'Sharpe ratio', and would like to know the 'standard' method for computing the same: Based on daily returns? Monthly? Weekly? ...
14k views

### Delta of binary option

What is the Delta of an at-the-money binary option with a payo out $0$ at $<100$ dollars, and payout $1$ at $>100$ dollars, as it approaches expiry? This is from a sample interview exam. I ...
10k views

### Best method for interpolating yield curve? [Multiple questions]

I'm building a spot curve for US Treasuries. My original selection of cash treasury include all the on-the-run bills, notes, bonds from 6 months to 30 years, as well as some selected off-the-run ...
4k views

8k views

### How to calculate US treasury total return from yield?

I'm struggling to understand the meaning of US treasury total return. What is easily available to get is yield data. Yield can be directly translated to the bond price at that time. In other words, ...
4k views

### American Options relation between greeks

Considering an American option in a Black-Scholes model, is there a relation between Vega and Gamma as it holds in the European case? I am aware an exact relation would be difficult to find. But in ...
1k views

### Obtaining risk-neutral probability from option prices

Suppose I have the following data (for the current stock and option prices of the Bank of America) Strike Last IV Probability 4 8 5.43 0.5813566 0.0000000 7 11 2.45 0.2868052 ...
922 views

### European Call Option Delta Upper Bound

For a pure equity process (with interest rate, dividend, etc., being zero) not necessarily the geometric Brownian motion, is the delta of a European call option always no higher than $1$? I am NOT ...
533 views

### Intuitive explanation of stochastic portfolio theory

Fernholz and Karatzas have published various papers about so called stochastic portfolio theory. Basically they say that the return to be expected from a portfolio on the long run is rather the ...
565 views

### Pricing VIX Futures

In a 2006 paper Zhang and Zhu propose a model for VIX and VIX Futures based on Heston. I am struggling in understanding how they get equation 6 and 8 (where they define the parameters). Can anyone ...
9k views

### Ways of treating time in the BS formula

The Black-scholes formula typically has time as $\sqrt{T-t}$ or some such. My questions: What is the granularity of this? If we treat $t$ as the number of days, then logically on the day of expiry, ...
1k views

870 views

### Put-Call relationship for Option on Forward

The forward price of a forward contract maturing at time T on an asset with price St at time t is, $$F=S_te^{(r-q)(T-t)}$$ where $r$ is the risk free rate and $q$ is the continuous dividend rate ...
1k views

### Calculating the pricing error in Fama-Macbeth Regression for Fama/French 5 Factor model

I'm very much new to this area and I need to know on how to calculate the pricing error in Fama/French 5-Factor model. The evaluation was done using the Fama-Macbeth approach. I did everything as ...
183 views

### Motivation of the singular perturbation solution formulation for local volatility model

I am puzzled by the motivation of the particular choice of the (singular) perturbation method used in Equivalent Black Volatilities. Equation (A.6a) sets $$\epsilon:= A(K)\ll 1.$$ What is the ...
1k views

### How many monte carlo runs do I need for pricing a Call?

I have to price several calls using Monte Carlo. Obviously, there is a huge tradeoff between the number of runs and the fair price of the call option. I know I can check how the approximation changes ...
4k views

### Prove that the butterfly condition is always greater than zero

I need to prove that the butterfly condition is always positive under no arbitrage theorem. We are constructing a long butterfly using European call options ...
221 views

This is a follow-up question on Price of a prepayment-based claim. Consider a zero-coupon bond of maturity $T$ with price $P_0$ for which the borrower can reimburse the principal $N$ at any time $\... 3answers 20k views ### Difference between CAPM and single index model which is the difference betwee a model like CAPM and a single index model? Is the first a special case of the second? Best 1answer 3k views ### Risk Free Rate vs LIBOR Theoretically, in pricing derivatives, most textbooks refer to the risk-free rate. What is obtainable in practice? The risk-free rate or the LIBOR rate? 2answers 670 views ### Verifying an identity of an equation for Black Scholes formula I just started working on the Black Scholes formula with help of the book Financial option valuation by Higham. Apparently you are possible to derive the following function:$\log(\frac{SN'(d_1)}{e^{-...
Prompted by a question that came up in the comments here, namely why we can apply the Ito lemma to a function of the form $f(x)=(x-K)^{+}$, I would be interested in knowing what are the least ...