# Questions tagged [mathematics]

The tag has no usage guidance.

160 questions
Filter by
Sorted by
Tagged with
36 views

### How to Compute and Understand Probability [closed]

After leaving school for 6 years, I'm reading the probability chapter from an interview book called A Practical Guide to Quantitative Finance Interview, and cannot make sense or understand how ...
172 views

100 views

### What the expectation of S^2 is from GBM? [closed]

I was at an interview and was asked to write down the SDE for GBM. $$dS = S\mu dt + S\sigma dX$$ Then I was asked how I would compute the expectation of S^2. I didn't know where to start. Any ...
127 views

386 views

### Mark Joshi, The concepts and practice of mathematical finance chapter 6 exercise 4

Let an asset follow a Brownian motion $$dS = \mu dt + \sigma dW$$ with $\mu$ and $\sigma$ constant. The constant interest rate is $r$. What process does $S$ follow in the risk-neutral measure? ...
295 views

### Mark Joshi, The concepts and practice of mathematical finance chapter 6 exercise 6 [duplicate]

Suppose a stock allows a geometric Brownian motion in a Black-Scholes world. Develop an expression for the price of an option that pays $S^2 - K$ if $S^2 > K$ and zero otherwise. What PDE will this ...
1k views

### How is stock data objectively different to this random walk?

I have a random walk that is generated as so using python, numpy, and matplotlib ...
148 views

### Mark Joshi, Chapter 5 Problem 2 of The concepts and practice of mathematical finance

If $$dX_t = \mu(t,X_t)dt + \sigma(X_t)dW_t$$ with $\sigma$ positive, show there exists a function $f$ such that $$d\left(f(X_t)\right) = v(t,X_t)dt + V dW_t$$ where $V$ is constant. How unique is $f$...
80 views

### CDS protection/contingent leg pricing, taking expectation of interest and hazard rates

The Pricing and Risk Management of Credit Default Swaps, with a Focus on the ISDA Model Screenshot: Pricing protection leg of a CDS, by OpenGamma In the screenshot above, I am having trouble ...
374 views

### 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 $1 d$- ...
I have this equation (Eq. (2.4) "The Volatility Surface - A Practitioner's Guide" by Jim Gatheral (Ed. 2006)): $$-\frac{\partial C(v, x, \tau)}{\partial \tau}+\frac{1}{2}v \frac{\partial^2 C(v,x,\tau)}... 6answers 15k 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? 0answers 202 views ### Optimal stop-loss reinsurance What are some methods for optimizing stop-loss reinsurance? I've found an article on the minimization of the variance. I also know about the method of average-at-range. Can we apply a method for ... 2answers 586 views ### Mark Joshi, Quant Interview Question problem 2.34; replicating a digital option on a 4-step symmetric binomial tree Question: Team A and team B, in a series of 7 games, whoever wins 4 games first wins. You want to bet 100 that your team wins the series, in which case you receive 200, or 0 if they ... 0answers 101 views ### Why do we have to use discretization methods for SDE? I haven't found the answer for the question above in google. Why can't we just discretize the equation instead of using methods like euler or milstein for the discretization. 2answers 804 views ### PDE pricing of barrier options in BS Path-dependent options in BS framework is intuitive to price with monte-carlo under risk-neutral measure, however it appears that several kinds can be priced with PDEs. I understand how does the story ... 1answer 134 views ### How to run optimization to achieve an equal active weight portfolio? I am trying to build an equal active weight portfolio, while minimizing the total risk. However, my constraint of equal active weight always leads to 0 active weight for everything. I know 0 active ... 1answer 33 views ### Calculating the ideal initial capital value to optimize a growth model I'm trying to work out a method for finding the initial capital value that allows someone to run out of money at the exact time they reach mortality. Currently, I'm graphing the annual total capital ... 2answers 429 views ### 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? 1answer 276 views ### Likelihood Ratio Method - Delta I was checking Glasserman(2004) - Monte Carlo for Financial Engineering and got to the likelihood ratio method. I am also looking in my textbook (M. Cerrato: The Mathematics of derivatives securities ... 1answer 757 views ### Intuition behind log return of portfolio = weighted sum of log returns Suppose we have n assets, each of which has weight w_i in the portfolio. The log return of asset i is denoted by r_i. What's the intuition why this holds approximately:$$ ln \left( \sum_i ...
Corporation $A$ has an excellent credit rating and can borrow at a fixed rate of $5\%$ or a floating rate of LIBOR + $1\%$. Corporation $B$ has a somewhat less excellent credit rating and can borrow ...