# All Questions

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### 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 ...
3k views

### Calendar Arbitrage in a Vol Surface

I am trying to determine the condition such that my implied vol surface doesn't have calendar arbitrage. I have done research and found that one such condition is that total variance should increase ...
6k 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, ...
2k views

### Arbitrage Free Volatility Smile

When ATM implied volatility is higher than OTM put and call I believe that the volatility smile is no longer arbitrage free? Why is that? On the other hand, when ATM implied volatility is lower than ...
733 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 ...
8k 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, ...
895 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 ...
489 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 ...
15k 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 ...
609 views

### Why is the GARCH intercept supposed to be strictly positive?

Maybe it's a simple question but I don't really understand why it is theoretically required. Let's take the standard GARCH(1,1) $$\sigma^2_{t+1}=\omega+\alpha\epsilon^2_{t}+\beta\sigma^2_{t}$$ In most ...
5k views

### What is an efficient method to find implied volatility?

I have a code that finds the implied volatility using the Newton-Raphson method. I set the number of trial to 1000 but sometimes it fails to converge and doesn't find the result. Is there a better ...
2k views

### Dynamic Hedge of Quanto Options

Can anybody explain to me step-by-step how can I dynamically hedge and/or replicate a quanto option with the foreign underlying asset, the foreign cash account and the domestic cash account as ...
750 views

### Importance Sampling for pricing options with longstaff and schwartz

I have been asking this similar question before. However, I really want to be concrete and get and concrete explanation. I have been reading the paper by Moreni and try to implement the same ...
5k views

### Calculate strike from Black Scholes delta

I have a list of deltas and their corresponding volatilities in an FX market but I want to go from delta to strike price. In this Question similar problem is being discussed How can I calculate the ...
7k views

### Implied dividend estimation

I am looking at two different ways of estimating the expected / implied dividends from market data. 1. Dividend futures I know that this asset class is not very liquid and might not be ...
7k views

### How does Cornish-Fisher VaR (aka modified VaR) scale with time?

I am thinking about the time-scaling of Cornish-Fisher VaR (see e.g. page 130 here for the formula). It involves the skewness and the excess-kurtosis of returns. The formula is clear and well ...
293 views

### Jim Gatheral's ansatz

In the Ansatz section of Jim Gatheral's book Volatility Surface (page 32), he assumes $$\mathbb E[x_s|x_T]=x_T\frac{\hat w_s}{\hat w_T}$$ where $\hat w_t:=\int_0^t \hat v_s ds$ is the expected total ...
3k views

### How to use the stock as a numeraire to price a derivative with payoff of the form $(S_T f(S_T))^+$?

I have $\frac{dS_t}{S_t} = rdt + \sigma dW_t$ as usual under the money-market numéraire and I need to price options with payoffs $$(S_T f(S_T))^+$$ How do I express the stock dynamics using the ...
7k views

### Proof of gamma profit formula

http://www.volcube.com/resources/options-articles/gamma-hedging-trading-strategies-part-i/ I would like to have proven to me the above formula, mostly because I don't quite understand it. The formula ...
1k views

### Black-Litterman, how to choose the uncertainty in the views $\Omega$ for smooth transitions from prior to posterior

In Black-Litterman we get a new vector of expected returns of the form: \begin{align} \Pi_{BL} = \Pi + \underbrace{\tau \Sigma P^T[P\tau\Sigma P^T+\Omega]^{-1}}_{\text{correction}}[Q-P\Pi] \end{align} ...
136 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 ...
814 views

3k 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 ...
410 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 ...
185 views

144 views

### How far the spot price is likely to go from the current level in three months if its volatility is 15.7%

On Page 24 of N. Taleb's "Dynamic Hedging" the author gives the following example Example: Assume that an asset trades at \\$100, with interest rates at 6% (annualized) and volatility at 15.7%. ...
120 views

### Exotic option arbitrage

Suppose an exotic European option has a sub hedging (price being lower than the target) portfolio of vanilla European options all with the same expiry as the exotic option. The sub hedging portfolio ...
164k views

### How can I go about applying machine learning algorithms to stock markets?

I am not very sure, if this question fits in here. I have recently begun, reading and learning about machine learning. Can someone throw some light onto how to go about it or rather can anyone share ...
4k views

### What papers have progressed the field of quantitative finance in recent years (post 2000)?

My question is pretty simple: what papers do you feel are foundational to quantitative finance? I'm compiling a personal reading list already, drawn from Wilmott forums, papers referenced in ...
23k views

### How to build a factor model?

Factor models such as Fama-French or the other ones that are partially summarized here work on the cross-section of asset returns. How are the factors built, how are sensitivities/coefficients ...
4k views

### How do you mix quantitative asset allocation with qualitative views?

Usually in asset allocation you have a quantitative approach (which can be from example mean-variance), but you (or you and your firm) also have a more qualitative approach given market-conditions, ...
34k views

### How to identify technical analysis chart patterns algorithmically?

I'm working on a small application that will provide some charts and graphs to be used for technical analysis. I'm new to TA but I'm wondering if there is a way to algorithmically identify the ...
9k views

### What types of neural networks are most appropriate for trading?

What types of neural networks are most appropriate for forecasting returns? Can neural networks be the basis for a high-frequency trading strategy? Types of neural networks include: Radial Basis ...
27k views

### Why does the minimum variance portfolio provide good returns?

I've been a researching minimum variance portfolios (from this link) and find that by building MVPs adding constraints on portfolio weights and a few other tweaks to the methods outlined I get ...
8k views

### Which approach to estimating fundamental factor models is better, cross-sectional (unobservable) factors or time-series (observable) factors?

There are many approaches to estimating fundamental factor equity models. I would like to focus on two traditional methods: The time-series regression approach of Fama and French. Factors are ...
4k views

### Separating the wheat from the chaff: What quant methods separate skillful managers from lucky ones?

Fund managers are acting in a highly stochastic environment. What methods do you know to systematically separate skillful fund managers from those that were just lucky? Every idea, reference, paper ...
61k views

### Where to get long time historical intraday data?

I am looking for long time historical intraday day data on the S&P500 composite for a time horizon like 10 years with a - for example 10-minutes tick - or prices for call/put options on the S&...
13k views

### What tools exist for order book analysis and visualization?

What tools exist for order book analysis and visualization? In particular, if one wanted to examine a limit order book and understand how it changes throughout the day where would you turn for ...
7k views

### How 'High' is the frequency in HFT?

How many trades per second are we talking about? What kind of strategies are used in this time frame? Can the small guy play the game?
26k views

### What is the best data structure/implementation for representing a time series?

I was wondering what is best practice for representing elements in a time series, especially with large amounts of data. The focus/context is in a back testing engine and comparing multiple series. ...
5k views

### Random matrix theory (RMT) in finance

The new kid on the block in finance seems to be random matrix theory. Although RMT as a theory is not so new (about 50 years) and was first used in quantum mechanics it being used in finance is a ...
4k views

### Why do expected return models and risk models use different factors?

This is a question responding to weekly topic challenge. I happen to see an interesting question from SYMMYS by Michael Kapler. I always approached expected return and risk modeling as separate ...
17k views

### What are the advantages/disadvantages of these approaches to deal with volatility surface?

I would like to know if someone could provide a summarized view of the advantages and disadvantages of the approaches on the volatility surface issues, such as: Local vol Stochastic Vol (Heston/SVI) ...