# Questions tagged [finance-mathematics]

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### Should we use the conditional expectation to write the value of an option?

So, I've just started looking into financial mathematics and the following question keeps bugging me. From what I understood, if the market is arbitrage-free and a given contingent claim of value $h$ ...
29 views

### Calculating market risk premium and expected excess return? [closed]

I need some help with this calculation. Suppose that the CAPM is valid and that the market portfolio consists of 60% stocks and 40% bonds. The standard deviation of the returns on stocks and bonds ...
42 views

### How to measure the difference between the trend of two curves

I'm looking for a way to measure the trend of two curves. For example, the figure below is my forecast for the S&P 500. It can be seen that although I haven't predicted the exact index price, the ...
1 vote
66 views

### Vasicek interest rate of T-forward measure [closed]

I know dr of risk-neutrual measure is There is a price of a pure-discount bond can be derived by computing the expectation, I get: where A and B are: why dr becomes to: under T-forward measure?
112 views

### Macaulay Duration - Liability matching

Can someone provide a detailed example to prove the following statement: "When the investment horizon is equal to the Macaulay duration of the bond, coupon reinvestment risk offsets price risk.&...
91 views

### How did Bachelier characterize the Brownian motion?

The model for a stock price $$dS_t=\mu dt + \sigma dB_t$$ where $B_t$ is a Brownian motion on $(\Omega, \mathcal{F},P)$, is commonly attributed to the work that Bachelier has carried out in his PhD ...
26 views

### What is the Accumulation/Distribution formula doing geometrically?

My understanding of the essence of the Accumulation/Distribution Index is that it tracks the closing price of a security during each period relative to its price range for that period, something like ...
56 views

### What could be a real-life example of sectors and instruments in a Financial Market in the context of this Portfolio Optimization Problem?

Recently I've been reading about mathematical models in finances and economics; however, I encountered this book chapter: Nagurney, A. (1993). Financial Equilibrium. In: Network Economics: A ...
1 vote
51 views

### Does a bond pay a coupon at maturity? [closed]

I know a bond pays an annuity cashflow of coupon payments and then at maturity it pays the face value. But, at maturity, does it pay an additional coupon payment on top of the face value or are we ...
61 views

### Elliott and Kopp Mathematics of Financial Markets confusion about proof of Lemma 2.2.5

In the book "Mathematics of Financial Markets" by R. J. Elliott and P. E. Kopp, Second Edition there is a claim made in the proof of Lemma 2.2.5., namely that $V_0(\theta)=V_0(\phi)$. I don'...
1 vote
48 views

I'm currently trying to implement the roll measure adapted by Easley et al. (2020, p. 22). https://papers.ssrn.com/sol3/papers.cfm?abstract_id=3345183 The adapted roll measure is given by the eq below....
21 views

### Counterparty Credit Risk - Reference book for a mathematical introduction [duplicate]

Which book would you recommend for an introduction to CCR from a mathematical perspective? I would like to complement the Jon Gregory's book "the XVA Challenge" with a more quant oriented ...
1 vote
146 views

### Game theoretic description of stock market

I read the book "Theory of Games and Economic Behavior" by John von Neumann and Oskar Morgenstern. I think that stock market may be described by game theory. But here are the problems: ...
1 vote
61 views

246 views

### Proving the discounted stock price is martingale

Let $\mathcal{K}_s$ be $$\mathcal{K}_s=\{\tilde{V}_t(\theta):0\leq t<\infty,\,\theta\text{ a simple strategy}\},$$ where $\tilde{V}_t(\theta)$ is the discounted value process of the self financing ...
281 views

### Explanation for Different Piecewise Yield Term Structures from QuantLib Python

I am new to QuantLib on Python, but as far as I understand, there are different types of piecewise yield term structures which exist on QuantLib which are bootstrapped on a number of interest rate ...
266 views