Questions tagged [finance-mathematics]

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votes
1answer
142 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 ...
1
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1answer
145 views

Calculating a VWAP using close prices snapshot

I was wondering, is it possible to calculate a daily VWAP (Volume weighted Average Price) from the close snap shot (close price, high, low open and total volume traded over the day)? If so is there a ...
2
votes
1answer
132 views

Cadlag Property of Jump Proccesses

I've recently started studying Cont & Tankov's "financial modelling with jump processes". I'm curious as to why that this assumption of the cadlag property (also called RCLL "right continuous ...
0
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1answer
84 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 ...
1
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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 ...
3
votes
1answer
258 views

Mathematical equation relating $\frac{dV}{dS}$ to $\frac{dV}{dK}$

Please help me figure out what is the mathematical relationship between $\frac{dV}{dS}$ (Delta) and $\frac{dV}{dK}$ ($K$=strike), taking into account vol skew. I ask this because I want to figure out ...
0
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1answer
69 views

What relevance might the Modigliani-Miller theorem have for weight of evidence?

Suppose in computing weight of evidence based on financial ratios of some bank, one finds that their debt ratio and equity ratio have largely (you pick how large I guess) differing weights of evidence....
3
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4answers
349 views

Mark Joshi Quantitative finance numerical techiniques, writting an algorithm that produces a random variable

Background: I am preparing for interviews and I was told to try and answer as many problems in the Mark Joshi book as possible. Question: Suppose an asset takes values from a discrete set $v_j$ ...
4
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1answer
671 views

Finding arbitrage opportunity

Find an arbitrage opportunity in this market. Can anyone explain how to mathematically solve this exercise with for example solving a system of linear equations?
1
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0answers
75 views

Moving average variance [closed]

I have generated a random series of returns drawn from a normal distribution and generated a random price series by compounding these returns (X) so $P_i = P_1(1+X)^i$. I want to show the analytic ...
-1
votes
1answer
47 views

How to calculate daily interest at different rates each day? [closed]

I have the following issue: I need to calculate the daily income of a financial application over a period based on a percentage of a daily financial index. The problem is that for each day, this ...
3
votes
2answers
286 views

Equivalent martingale measure price dynamics

Assume $S_0(t)=\exp(\int_0^t r(s) ds)$. Then $\mathbb{Q}\sim \mathbb P$ is a martingale measure $\iff$ every asset price process $S_i$ has price dynamics under $\mathbb Q$ of the form $dS_i(t)...
1
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1answer
55 views

Thorp's var caclulation

I have been working through Thorp's paper, and with some guidance have got as far as page 20, but I am now stuck with Thorp's result in Ex 6.2 (on that page) where I cannot get the result for $Cor(X_1,...
0
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1answer
87 views

Kelly Variance - variance of the sum of logs

I am working through Thorpe's Ch 9 on the Kelly criterion. On page 9 Thorpe states: $$Var(ln(1+Y_if)] = p[ln(1+f)]^2 + q[ln(1-f)]^2 - m^2$$ Since $var(X) = E[X^2] - m^2$, $$p[ln(1+f)]^2 + q[ln(...
0
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0answers
63 views

CAPM Beta zero-correlation performance issue

I am working on a research project that requires me to run a CAPM regression on all intra-day stock quotes in NSDAQ, NYSE and all other U.S. exchanges since 1993. The precision of the quote data is ...
1
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0answers
99 views

Kelly's maximum for G(f)

In Thorpe's paper, Thorpe derives the Kelly criterion $$f^* = p - q$$ and plugs this into the equation $$G(f^*) = p \times \log(1+f^*) + q \times \log(1-f^*)$$ to get the following expression $...
1
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1answer
144 views

MATLAB exercise on an European call option with time-varying volatility

I have to solve the following exercise: compute and plot the value $V = V(S, t),\ t<T$, ($T=$ maturity) of an European CALL option (with arbitrary $t$, $T$, $K$ (strike price), $r$ (risk-free ...
-3
votes
1answer
123 views

Put Call Parity confusion [closed]

My question concerns an ambiguity in the wikipedia article about Put Call Parity. In the first sentence: "In financial mathematics, put–call parity defines a relationship between the price of a ...
8
votes
1answer
299 views

Replicating a portfolio with a certain payoff function

Assume there are two stocks $S_1$ with price $p_1(t)$ and $S_2$ with price $p_2(t)$ where $t$ indicates time. Assume, there is a hypothetical derivative $D$, which is such that, price of $D$ at a time ...
3
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0answers
165 views

reference for portfolio / margin calculations in backtesting tool

I have been tasked with writing a backtesting tool from scratch. I understand a lot of trading operations, but I am primarily a researcher. I need to support futures and equities trading. I need to ...
0
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0answers
121 views

How to consider open interest & volume change in option pricing?

Is there publically available option pricing model or theory that considers open interest/volume % change? I believe that laws of supply and demand effect options like any tradable good. However, I ...
2
votes
1answer
353 views

CAPM Calculations

Im trying to calculate Alpha using CAPM & I have data on everything necessary. $$R_t-R_f={\alpha}+{\beta}\times(R_m-R_f)$$ i.e. $${\alpha}=R_t-R_t-{\beta}\times(R_m-R_f)$$ In more detail, I ...
1
vote
1answer
284 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 ...
1
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1answer
540 views

Shall I use the Longstaff and Schwartz method or the forward Monte Carlo method to price an American call?

I am comparing two methods: Least squares by Longstaff and Schwartz and A Forward Monte Carlo method. I am not sure what price I should consider as the "true value" to compare these two approaches. ...
1
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1answer
3k views

Swap contract comparative advantage

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 ...
0
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1answer
850 views

Pathwise Derivative To Estimate Delta

I am trying to estimate delta using the pathwise derivative method (Broadie and Glasserman (1996)) and I stuck on this part: Here is the other notation defined: Here is my C++ code I have written so ...
4
votes
1answer
514 views

European call delta derivation

Let's write $S(T) = S_T$ and $S(0) = S_0$. We want to compute $\frac{d}{dS_0}\mathbb{E}[f(S_T)]$. From a previous discussion this is equal to $$\mathbb{E}_{S_0}\left[f(S_T)\frac{g'_{S_0}(S_T)}{g_{S_0}(...
1
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1answer
251 views

Extending risk neutral measure to insurance/mortality filtration

In insurance mathematics, one often models the underlying of an insurance policy with a Black Scholes model on a filtered probability space $(\Omega,\mathbb{Q},\mathcal{F},\mathbb{F}=(\mathcal{F}_{t}))...
0
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0answers
143 views

Portfolio with several risky assets and one risk-free

Suppose we have $N$ risky assets $r_1$, $r_2$, ... , $r_N$ with a covariance matrix C. If we want to build a portfolio $\omega = (\omega_1, \ldots, \omega_N)^t$ (I loosely denote the portfolio with ...
2
votes
2answers
115 views

Force of interest third degree polynomial

Just struggling with a question here, any help would be appreciated. For its deposits, a bank offers a force of interest per annum over a given year, which equals 4.99% at the beginning of the year, ...
2
votes
1answer
238 views

Using crude Monte Carlo

Background Information: The crude Monte Carlo algorithm for the arithmetic Asian call option is $$Y = e^{-rT}(\overline{S}_A - K)^{+}$$ and the control is $$C e^{-rT}(\overline{S}_G - K)^{+}$$ The ...
0
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1answer
441 views

Dividend yield under Black 1976 formula for futures options?

I have a question regarding the BS 1976 formula for futures options. https://www.glynholton.com/notes/black_1976/ How do I deal with dividends under this model, assuming that the dividend yield is ...
0
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1answer
67 views

Valuation functional

Consider an economy with $J = 2$ assets and $S = 3$ states. The $J\times S$ payoff matrix for the two assets is $$X = \begin{pmatrix} 0 & 3 & 3\\ 1 & 1 & 0\\ \end{pmatrix}$$ and the ...
1
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1answer
193 views

A forward Monte Carlo method for American Options Pricing

I am trying to implement the forward Monte Carlo algorithm from the paper "A Forward Monte Carlo Method for American Options Pricing" by Daniel Wei-Chung Miao and Yung-Hsin Lee. I am a little bit ...
1
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0answers
191 views

What jobs in Finance are most math intensive? [closed]

I'm a math major and I've always been really interested in Finance; however, I'm starting to enjoy math more and more and would like to know which jobs in Finance use the most/more advanced math. Also,...
-2
votes
1answer
677 views

Which book would you recommend for beginners in Quantitative Finance? [closed]

I have a normal high school level of mathematics including some statistics and find the world of Quantitative Finance both alien and invigorating at the same time so, would like to learn more. What ...
1
vote
1answer
234 views

Monthly returns annualized vs annual returns [closed]

Lets say that I have a stock with annual returns, $a_i $ for year $i\in \left\{1,...n\right\}$ and monthly returns $m_{i,j}$ for month $j\in \left\{1,...12\right\}$. Lets define monthly returns to be ...
3
votes
2answers
468 views

Why are some utility functions widely used?

There are some von-Neumann utility functions that I come across quite often in different articles / books like: $ U(x)=\ln(x)$, $U(x)= \frac {1}{\gamma}x^\gamma$ with $\gamma <1$ and $U(x)=\frac {1-...
2
votes
1answer
98 views

Is there a quick way to see why this claim $C(S, t)$ on $S$ does not satisfy the Black-Scholes PDE?

I'm self-studying for an actuarial exam on financial economics and encountered the below practice exam problem. An exam problem should typically take 5-6 minutes to complete, so I'm wondering if ...
2
votes
1answer
89 views

Transform raw forecasts into orthogonal forecasts

I am trying to combine multiple forecasts on each of N assets in line with Grinold and Kahn's methodology, taken from Active Portfolio Management, 2nd ed. On p.311, they suggest transforming the raw ...
1
vote
1answer
797 views

Given two risky stocks calculate the rate of return, standard deviation, beta, and risk-free rate

Consider a world where there are only two risky stocks, $A$ and $B$, whose details are listed in the table below: Furthermore, the correlation between the returns of stocks $A$ and $B$ is $\rho_{A ...
0
votes
1answer
196 views

Using CAPM to derive the following

Background Information: Say there are $s = 1,\ldots,S$ possible future outcomes (states) with known probabilities $\pi_s > 0$, $\sum_{s=1}^{S}\pi_s = 1$. Define the expected payoff as $\mathbb{E}_\...
3
votes
1answer
209 views

Payoff of European Call Option with Transactioncosts

I was wondering about the following scenario: assume that you have a underlying which trades under a positive bid-ask spread $S^B \leq S^A$ and that there is also a European Call-Option on this ...
1
vote
0answers
95 views

Can someone suggest some good reads on OAS and Spread Duration?

I have been through the CITI Yield book paper and the OAS by Barclays. Is there is anything else that tackles this topic? Any help would be much appreciated. Cheers!
5
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2answers
6k views

What is the difference between pull to par and roll down in both mathematics and conceptual?

I don't really understand the difference. Shouldn't roll down and pull to par be the same technically? If a bond is trading as a discount it "increases" in value because everyday gets closer to par, ...
3
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2answers
579 views

Is mathematical finance relevant in asset managament?

I was hoping to consult on the relevance on the relevance of mathematical finance in the asset management business. Traditionally, mathematical finance focuses more on topics related to stochastic ...
1
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0answers
359 views

Different definitions of arbitrage

Consider the following setup: Let $S=\left(S_1,\ldots,S_n\right)$ be a $n$-dimensional price process and denote by $V$ its value process defined by $V_t=\phi_t\dot\ S_t$ for $t=0,\ldots,T$. In "...
0
votes
1answer
499 views

How to price 0 floors in csa agreements for negative ois rates?

A CSA (Credit Support Annex) agreement specifies the interest rate to be earned on the collateral provided to back a derivatives transaction. For cash collateral this rate is generally the OIS (...
2
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0answers
187 views

How to understand the integral in the Girsanov theorem?

Let $W^P$ be a $d$-dimesional $P$-wiener procss. Define $L_t = > e^{\int_0^t \phi_s^T dW_s^P - \frac{1}{2} \int_0^t \| \phi_s\|^2 > ds}$.Assuming $E^PL_T = 1$, then the measure given by $dQ = ...
0
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0answers
54 views

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 ...