# Tagged Questions

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88k 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 ...
8k views

### Recommendations for books to understand the math in quantitative finance papers?

Can anyone recommend books that explain the math used in quantitative finance academic papers?
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### 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 ...
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### How random are financial data series?

Pseudorandom number generators are often tested using e.g. a test suite like Diehard tests or Dieharder. If one would run these tests e.g. on stock market time series or other financial data, would ...
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### Any recommendations for textbooks for an undergraduate course in mathematical finance? [closed]

I'll teach an introductory course on mathematical finance in the near future. The course is intended to entertain and broaden some well-prepared advanced undergrad mathematics majors, some physics ...
7k views

### What is a martingale?

What is a martingale and how it compares with a random walk in the context of the Efficient Market Hypothesis?
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### Why Ito calculus?

Coming from physics, I am used to the fact that the Ito interpretation of most natural stochastic equations is wrong, and one should be using Stratonovich calculus instead (of course they are ...
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### Is a linear combination of GARCH processes also a GARCH process?

If two time series follow a GARCH process, and a third is a linear combination of them, is the third also GARCH process?
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### Is it possible to understand financial theory without mathematics?

I am trying to develop a short course on financial theory, covering the fundamentals of forward and options pricing, and 'efficient market' theory. I want to reduce the amount of mathematics to a ...
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### Proving the asymptotic distribution of Manipulation-Proof Performance Measure (MPPM) (Paper by Goetzmann et al.)

In Goetzmann et al.'s (2007) paper, the authors derive a "Manipulation-Proof Performance Measure" (MPPM), which is a performance measure that is impervious to performance manipulation by fund managers....
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### When pricing options, what precision should I work with?

I'm wondering if there's any point at all in double-precision calculations, or whether it's ok to just do everything in single-precision, seeing how the difference on non-Tesla GPUs for single and ...
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### Modified Durations of Different Noncallable Bonds and function of Maturity

I'm hoping someone could help me understand this subject better. Basically I am reading a book and it shows a table ...
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### What are the options for a mathematician to break into QF without working for a fund?

I have a degree in mathematics, and I've worked as a statistician and done some programming work. I'm very strong in my math/stats/programming background and have browsed some QF books, and I'm very ...
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5k views

### Hurst Exponent Calculation

I am trying to calculate the Hurst Exponent using Excel. I am facing a problem where the exponent value sometime goes beyond 1. Can someone share a link / material so that it will help me to calculate ...
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### Value of European Call equals Value of American Call, Question on Explanation/Proof

I am reading S. Shreve, Stochastic Calculus for Finance, Vol. I. There he proves that American Call Options have the same value as European Call Options. In the proof he uses that for a Call option ...
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### FTAP in the model independent case, paper by Schachermayer

I have a question about the following paper by Beatrice Acciaio, Mathias Beiglböck, Friedrich Penkner, Walter Schachermayer. At the very beginning of the paper, on page 3, there are two definitions ...
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### Foward-start option pricing

Consider a probability filtred space $(\Omega, \mathcal F, \mathbb F, \mathbb P)$, where $\mathbb F = (\mathcal F_t)_{0\leq t\leq T}$ satisfing the habitual conditions and is generated by $1 d$- ...
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### Monty Hall Model

Given a fixed time period,say 3 days, the stock/market can go up,down or stay sideways. A hedge fund can long, short or use rangebound(options strategy) to bet for that 3 days closing level. Hedge ...
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### Distribution of minimum of hazard functions

Suppose I have two random variables, $X_1$ and $X_2$, that are independent (but not identically distributed) and assume both have hazard functions $\lambda_1(s)$ and $\lambda_2(s)$, for $s > 0$. ...
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### Linear combination of Payoffs using Black-Scholes

Write the payoffs in Figure 3.8 as linear combination of call options and derive a closed form formula for the Black-Scholes price, the Delta, and the Gamma of them. All the Greeks of the option are ...
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### Pricing digital options in discrete time

I am stuck in this exercise from my textbook: Consider a one-period market model with $N+1$ assets: a bond, a stock and $N-1$ call options. The prices of the bond are $B_0=1$ and $B_1 = 1+r$, ...
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### Trinomial model converges to Black-Scholes weakly

Consider risk-neutral trinomial model with $N$ periods presented by $$S_{(k+1)\delta}H_{k+1}, \ \ \text{for} \ \ k=0,\ldots,N-1$$ where $\delta:=\frac{T}{N}$ and $\{H_k\}_{1}^{N}$ is a sequence of i....
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### Black-Scholes Equation with dividend

Consider a European option with payoff $$g(S_T) = S_T^{-5}e^{10S_T}$$ Assume that the interest rate is $r = .1$ and the underlying asset satisfies $S_0 = 2, \sigma = .2$, an pays dividend at ...
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### $\frac{1}{p(T_{i-1},T_i)}(A-p(T_{i-1},T_i))^+$ at time $T_i$ is equivalent to a payment of $(A-p(T_{i-1},T_i))^+$ at time $T_{i-1}$

How can I show that payment of $\frac{1}{p(T_{i-1},T_i)}(A-p(T_{i-1},T_i))^+$ at time $T_i$ is equivalent to a payment of $(A-p(T_{i-1},T_i))^+$ at time $T_{i-1}$ ? Where A is a deterministic constant....
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### Arrow-Debreu Equilibrium Pricing

I have this problem in asset pricing that I don't know how to solve. Here it is: Consider an economy with a complete set of Securities and $N$ states of the world Tomorrow. Assume that there are two ...
Some notation: We consider a financial market with $d+1$ assets, the $0$-th asset is considered the risk-free asset, the others are the risky ones. The vector $\overline \pi \in \mathbb R^{d+1}$ ...