# Questions tagged [finance-mathematics]

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### Concatenation property of a set of semimartingales

Consider as in (1, Definition 2.1) a convex subset $\mathcal{X}_1$ of the set of semimartingales $\mathbb{S}$ satisfying the following properties: $X_0=0$ $X_t\geq -1$ for all $t\geq 0$ for all ...
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### How to price a quanto basket option?

EDIT: Maybe there is no way to get explicit solutions for basket options (maybe the Black-Scholes differential equation can't be solved directly ??). Q3: How do you price and hedge ( S1(T) + S2(T) - ...
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### Step by Step Guide to Learn Quantitative Finance [closed]

Can some one help in creating step by step guide to learn Quantitative Finance? The suggestions should be in the lines of 1- Which Maths topics needs to be learn 1st 2- Which Maths Books or ...
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### Is Black-Scholes complete?

If we have a Black-Scholes model $B_t = \exp{(rt)}$ and $S_t = S_0\exp{(\sigma W_t + \mu t)}$ then is it complete? What if $W_1$ and $W_2$ are independent Brownian motions. Then the two-stage ...
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### Black-Scholes evaluating the squared of the stock price

Consider a Black-Scholes model $S_t = 5\exp{(\sigma W_t + \mu t)}$, $B_t = \exp{(rt)}$, where $W_t$ is Brownian motion with respect to a given measure $\mathbb{P}$. Suppose you hold a forward ...
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### For discrete models, the existence of strong arbitrage is equivalent to a particular self-financing strategy

Background Information: This question is from Lectures on Financial Mathematics: Discrete Asset Pricing. Question: Prove that for discrete models, the existence of a strong arbitrage is also ...
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### All martingale measures price the attainable claim equally

Background Information: This question is from Lectures on Financial Mathematics: Discrete Asset Pricing. Theorem 3.2 First Fundamental Theorem of Asset Pricing - Suppose $\nu$ is any measure such ...
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### Where can I find ideas for strategies? [closed]

Every book I read refers me to many other books, there is practically no way I can read all this text in my life time. Once and for all, where is the best place to fish for ideas?
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### Calculation of Weighted Interest Rate based on Outstanding Debt

I would like to know what's the way on how to calculate the weighted average interest rate for a loan portfolio properly, especially when looking at periods shorter than a year. The basic definition ...
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### Law of One price and the Inconcistent pricing strategy

Background Information: A market satisfies the Law of One Price if every two self-financing strategies that replicate the same claim have the same initial value. An inconsistent pricing strategy is ...
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### Price of every asset in discrete market model strictly increasing

If the price of every asset in a discrete model is strictly increasing, with probability one, then does the market admit arbitrage? Thoughts: I believe this is true but I am not sure how to give an ...
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### Zero-coupon Loan Investment [closed]

Zero-coupon default-free interest rates maturing over the next five years are listed below (in percent per annum, continuously-compounded): Maturity Years -- Yield 1 --------------------1.9 2 ------...
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### Formula for conditional expectation. Related to the Fundamental Theorems of Asset Pricing

Let $\lambda$ be a probability measure on $\Omega$ (finite), with filtration $\{\mathcal{F}_t\}$. Define $\nu(X) = \lambda\left(X\frac{d\nu}{d\lambda}\right)$, where $\frac{d\nu}{d\lambda}$ is a ...
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### Computing Buy-and-hold abnormal returns (BHARs) $= \prod_{t=\tau_1}^{\tau_2}(1+R_{i,t}) - \prod_{t=\tau_1}^{\tau_2}(1+R_{m,t})$

I am doing an event study and wanted to know if was going about this correctly$$\text{BHAR}_{i(\tau_1,\tau_2)}\quad=\quad\prod_{t=\tau_1}^{\tau_2}(1+R_{i,t})~-~\prod_{t=\tau_1}^{\tau_2}(1+R_{m,t})$$ ...
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### Verifying value of claim as an expectation

Background: We have so far taken the bond B to be deterministic for simplicity, but some reflection shows that this is not in any way necessary. Everything works out the same way with a stochastic ...
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### Can someone check this boundary condition for me?

At the moment I'm comparing plots between the implicit numerical Black-Scholes PDE and the Monte-Carlo Method for the Black-Scholes equation. However, for the particular boundary condition I'm using I'...
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### Can someone try this Boundary Condition for the Black-Scholes PDE out for me?

I have a bit of a favor to ask and if anyone could help me out with this I'd really appreciate it. At the moment I'm trying to use the triangle wave formula as the payoff for the Black-Scholes PDE i.e....
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### Initial/Boundary Conditions for a Butterfly Option?

What are the initial and boundary conditions for a Butterfly Option? I want to write up a PDE program for it and I have a rough idea of what the payoff should be (is it just a call and a put at the ...
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### Implied Expected Stock Return from European Option Prices

We can calculate the expected stock return (under the measure $Q$) from at-the-money ($K=S_t$) option prices as: $$E\left(\frac{S_T-S_t}{S_t}\right)=\frac{e^{rT}}{S_t}(C_t-P_t)$$ The result is ...
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### How can we observe volatility smile from the market. Drawbacks of Heston Stochastic Volatility Model

Here are two questions related to implied volatilities. a) The set up here is for an European option. We can get its implied volatility smile from calibration, the question is why could we also ...