# Tag Info

Accepted

### Preferred Option pricing model

General Comment: In industry, you're effectively an engineer/mechanic. You choose the best tool for the job, and there is no 1 tool that works with everything because they all have different benefits ...
Accepted

### Multicurrency holiday calendar math and combinations

FX is quite tricky here. There is also no complete agreement between market makers and regions. However, if you have access to Bloomberg, you can look up many rules on the help page of ...
• 9,014

### Why is the stochastic process of the volatility of a stock price square integrable?

You can define the Ito integral without square integrability but this makes working with applications like pricing more complicated, so the assumption is typically made in practice. The question of ...
• 1,727

### Multicurrency holiday calendar math and combinations

In my experience in trading FX Swaps, your description of the "Earliest Valid Day" is the probably the most accurate description but not the way you interpret it. In your example, if you ...
• 6,632

### Risk Neutral Pricing Exercise

A few comments: The question says "using Ito's lemma". We can also do it without using Ito's Lemma by simply calculating $E^Q(S_T^2)$ -- this should give you something that agrees with your ...
• 625

### Calculating spread on a par rate curve given bondâ€™s coupon and yield

Z-Spread or OA-Spread (with no optionality) In Python's rateslib you can make the following calculation: Define a bond and a <...
• 10.7k
Accepted

### Is sorting stocks into portfolio mandatory in Fama-French model?

When you only have three stocks in your data set, trying to form portfolios will not be helpful. Run the analysis on the individual stocks' data as is. Using portfolios instead of individual assets in ...
• 3,156

### QuantLib: How to bootstrap Yield Curve using 3M futures - Python

The theory and a worked-out example are in Ametrano and Bianchetti, Everything You Always Wanted to Know About Multiple Interest Rate Curve Bootstrapping but Were Afraid to Ask. Recently I reproduced ...
• 7,693

### Roll Critique - CAPM and mean variance tautology?

Let $R$ denote the vector of risky asset returns, $\Sigma:=\text{Cov}[R]$ the covariance matrix of returns, $\mu:=E[R]$ the vector of expected returns, and $r:=R_f$ the risk-free rate. Recall that the ...
• 131

### QuantLib: How to bootstrap Yield Curve using 3M futures - Python

If you want a really easy answer, you can do the following: Convert your futures prices into rates e.g. $100 - price = rate$. Construct a LineCurve in ...
• 10.7k

### How to find interesting open math problems in quantitative finance that I could publish articles about?

I think it is difficult to come up with an open problem in math finance that is also economically/socially relevant. And I don't mean to say "practitioner" relevant, as you mentioned you ...
Accepted

There is a big different between the financial intermediation (that can use a risk-neutral approach to prevent too large misalignment of valuations that would be due to disparities of risk aversions), ...
• 12.2k

### What are the downsides of using Kim's integral equation (1990) to determine the exercise boundary of an American option?

Note: the most popular approximation in quant libraries I have known is not from Kim (1990) but rather the Whaley approximation. There are several good reasons to prefer numerical PDE solvers over ...
• 14.9k
1 vote

### What is the proper way to derive risk definitions from utility functions?

My reply was too long, so I am posting it as a separate comment. Thank you Kermittfrog for the derivation! (I think you meant to write $\rho(W_0)$ instead of $\rho(w)$ in the value of $w^*$.) Since ...
• 73
1 vote
Accepted

### What is the proper way to derive risk definitions from utility functions?

Note: This is (still) the starting point to a proper answer. If time permits, I'll add some flesh from time to time. From a mathematical point of view, in order to obtain the optimal investment ...
• 6,737
1 vote
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### Possibility of obtaining a positive mathematical expectation in a quoted currency

When Siegel wrote his famous article in 1972, a widely accepted theory of forward rates was the Unbiased Expectations Hypothesis, that the forward price (or futures price) of a currency was equal to ...
• 11.4k
1 vote

The unique solution of the stochastic differential equation that is mentioned: $$dS_t = S_t\mu dt + S_t \sigma dW_t$$ is given by: S_T = Se^{(\mu - \frac{\sigma^2}{2})(T-t) + \sigma (W_T-W_t)}=Se^{(\...
• 21
1 vote

### Is this arbitrage? Infinite payoff / infinite loss (energy generation investment problem)

Arbitrage means that you can a profit (in at least some states of the world), without the risk of losing. IIUC, in your state 2, you'd make a loss, and the bigger your investment x, the bigger the ...
• 3,501
1 vote
Accepted

### Breaking down gamma PnL by time

Unless you are hedging your portfolio fully every hour, there are mutliple ways to attribute gamma PnL here, all of them are correct and incorrect at the same time. Your delta PnL is also coming from ...
• 68
1 vote

### Option pricing under distribution assumption

After reviewing further literature, I have come to the conclusion that indeed this method gives the correct answer. This thought process can be used to derive BS-formula, given the (risk-neutral) ...
• 175
1 vote

### Fama-French Regression Output Interpretation (Intercept/Alpha)

If the model holds, $\alpha_1=\dots=\alpha_N=0$ for all the test assets $i=1,\dots,N$. (In your case $N=3$.) Conversely, if $\alpha_i\neq 0$ for at least one asset $i$, the model does not hold. Now, ...
• 3,156
1 vote
Accepted

### How to calculate VaR given mean and sd?

It is really simple. The formula is just: $VaR_{\alpha,T} = -\mu T + Z_{\alpha} \sigma \sqrt{T}$ Take note the time horizons should match between the drift and the vol terms. Also VaR is usually ...
• 1,409
1 vote
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### Characteristic Function for Wishart Heston Model

I have solved the problem myself. In summary, one has to evaluate the complex matrix for each argument of the Fourier/Laplace transform $u_1, \dots, u_{1000}$. This cannot be done with MatLab's ...
• 66
1 vote