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8 views

Weak solution of a SDE

$\text { Consider the } \operatorname{SDE} d X_{t}=\operatorname{sign}\left(X_{t}\right) d t+d B_{t} \text { on } 0 \leq t \leq T, \text { where } \operatorname{sign}(x)=1\\ \text { for } x>0 \text ...
1
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0answers
11 views

Portfolios sorted by TED volatility

I was reading a paper titled "Betting against Beta" (link). The paper has five major propositions. The fourth proposition is that betas are compressed towards one when funding liquidity risk ...
1
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1answer
24 views

Options On Earthquakes

As a financial innovation, the options market is introducing Options contracts based on California Earthquakes. In your own words, discuss the following: True or False? “The sellers of Options on ...
0
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0answers
15 views

Why and when we should use the log variable?

Normally, I see finance papers use the real ratios but log regarding non-ratio variables. For example, Dasgupta, 2019 used log(asset) or log(1+firm age) or log GDP, but regarding the ratio, they use ...
0
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0answers
3 views

Calculate core deposit bucket percentages

I need to forecast core deposits in a commercial bank. One technique that I saw consists in dividing the amounts in buckets and applying a percentage to each bucket to obtain the core deposit. For ...
-3
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0answers
13 views

Risk neutral valuation and the drifts

I thought that for something to be risk neutral it had to drift at the risk free rate r dt (and plus a odw term) However, apparently if you calibrate a Heston model to market prices this gives you ...
0
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0answers
17 views

Mortage Backed Securities: interest-only (IO) and principal-only (PO) - Present Value

Does any of you know what are the PV (present value) mathematical equations for Interest Only, and Principal Only MBS's (assuming no prepayments, or defaults)? I am not familiar with Mortgages, so I ...
0
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1answer
40 views

FX hedged investments

I was reading FX hedged investments do not have an impact on the FX rate. For example, a Japanese fund buying US treasuries fully FX hedged. I understand the hedging is usually done through short term ...
0
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0answers
13 views

Arbitrage optimal size model that accounts for slippage given a specific path?

I'm interested in any model that helps calculating the optimal size to maximize PnL given the liquidity of an asset (or the slippage that I would incurr per unit of asset traded). For instance, let's ...
2
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2answers
75 views

Change of measure for a stochastic process to be a martingale

$\text { Give a measure change so that } X_{t}=e^{B_{t}}\left(B_{t}-t / 2\right) \text { is a martingale, } 0 \leq t \leq T$ My attempt Using Ito's lemma on $X_{t}$ we get: $-\frac{e^{B t}}{2} d t+\...
1
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0answers
47 views

Solving SDE Dubins-Schwarz Theorem

$\text{ Let } X_{t}=1+t+B_{t}, \text { and } T=\inf \left\{t: X_{t}=0\right\} . \text { Define } G(t)=\int_{0}^{t \wedge T} \frac{d s}{X_{s}}. $ $\text { Let }\ \tau_{t}=G^{-1}(t) \text { be the ...
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0answers
37 views

Calculating Counterparty Exposure of a collateralized Portfolio

What could be counterparty exposure on a portfolio where:- a. Client sells a put option on equity to us which is collateralized by corporate bond? b. Client buys a put option on equity from us which ...
0
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0answers
34 views

VaR of a Swaption Portfolio

How would we compute VaR of a Swaption Portfolio? a) Portfolio consists of a long Payer Swaption b) Portfolio consists of a short Payer Swaption. How would the VaR computation differ between the 2 ...
0
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0answers
48 views

Problem from Stochastic Portfolio Theory Textbook

I'm trying to do the following problem from Robert Fernholz's textbook Stochastic Portfolio Theory: The assumptions mentioned are: and my attempt is as follows: I have no idea how to deduce that ...
0
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2answers
85 views

Hull on Futures: I am not able to understand this sentence

The usual rule chosen by the exchange is to pass the notice of intention to deliver on to the party with the oldest outstanding long position. ...
2
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0answers
17 views

Should we include the industry variables when we control for year*industry fixed effects?

Normally, in panel data, we control for firms and years fixed effects even we also have some time-variant firm-level regressors. I am wondering whether it also happens at the industry level. If it is ...
2
votes
2answers
55 views

Deciding (p,q) in garch and model test on empirical data

I'm currently working on a dataset containing data from the 29 January till the 29 July 2009. In the dataset I have prices of the S&P 500 index for all days. Furthermore, I have the implied ...
-2
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1answer
84 views

Why continuously compounded interest a standard in finance? [closed]

Why is the "continuously compounded interest" the standard in finance? Many finance textbooks use the formula e^rt without justification. The assumption that the interest frequency is ...
4
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0answers
40 views

Bates Model on Quantlib

I am actively trying to price an option using bates model on Quantlib.However,when I input my volatility I find the same Black Prices with the basic Heston Model.I wanted to know if my code was right. ...
0
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1answer
77 views

Digital and binary put/call options

I'm looking for put-call parity for the call and put digital options, but I don't really know what is digital options and it's difference between ...
0
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0answers
21 views

SVAR, seasonality adjustment and impulse response functions

My question might be slightly dumb, however I could not find out which choice would be better. I am trying to construct a SVAR model including the french inflation rate, the unemployment rate and the ...
3
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0answers
57 views

Bet sizing with regression predicitions?

Applying the kelly criterion for bet sizing is quite easy if we use a (binary) classification model (say to predict the sign of a price return) or other model where probabilities of classes are a ...
1
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0answers
65 views

Changing order of integration on stochastic term in Vasicek

This question is in relation to the vasicek model, where i am trying to find the solution. I have this term: $-\int_{t}^{T} \sigma \int_{t}^{s} e^{-\kappa(s-u)} d W(u) d s$ I need to change the ...
0
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0answers
12 views

How to construct limit order book from order flow data?

I need to construct the limit order book for a specific stock at regular time intervals using order flow data. Is there a package or a built-in function that can do this?
3
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0answers
41 views

Interaction between raw position signals and portfolio optimisation methodologies [closed]

I'm trying to get my head around how the various aspects of constructing a final position generally interact and wonder whether anyone could expand on my (tentative) understanding currently. As I see ...
0
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0answers
24 views

CEV Model Pricing-Implied Volatility Surface

I am trying to validate a local volatility model (Dupire) and I was told to do the following in order to validate it. With a deterministic model as it is the CEV model, I have to price several options ...
0
votes
1answer
62 views

option pricing formula for $S_{t}=S_{0}+\mu t+\sigma B_{t}$ where r = 0

I have been on this for hours and it's not getting me anywhere. Any help is so highly and deeply appreciated. A call option with strike $K$ and expiration $T$ pays $C_{T}=\left(S_{T}-K\right)^{+}$ at ...
1
vote
1answer
57 views

HNGARCH Option Pricing in R (How to loop)

I am having difficulties when using the HNGOption program in R. The program will only run for 1 specific option price, meaning that I would have to manually insert strike price etc. and this would ...
2
votes
1answer
45 views

How to approximate a delta using monte carlo methods and finite differences via Higham's book?

I'm currently taking a Mathematical Finance module at University and one of the recommended texts is “An Introduction to Financial Option Valuation: Mathematics, Stochastics and Computation” by D.J. ...
3
votes
1answer
81 views

Calibrating Hull-White 1 Factor

I have been trying to learn HW1F on my own, out of nothing more than genuine curiosity during my twilight years, and I'm confused on the issue of calibrating. I don't know why, but all the research ...
0
votes
1answer
68 views

Generate FX Carry Return Index

I would like to generate a daily carry return index for a given currency pair - lets take USDEUR as an example. I presume this involves something like taking the spot rate and the appropriate funding/...
0
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0answers
34 views

Multidimentional Black Scholes Formula

I need to write the Black-Scholes formula for option $V = (S_1, S_2, t)$, where: $$d S_1 = \mu_1 S_1 dt + \sigma_1 S_1 d W_1,$$ $$ d S_2 = \mu_2 S_2 dt + \sigma_2 S_2 d W_2.$$ We know that $W_1$ and $...
0
votes
0answers
6 views

How to get the 3-digit SIC code from Datastream and merge ISIC to SIC?

When merging an ISIC-related dataset (dataset A) to a SIC-related Datastream dataset (Dataset B), I faced a problem with the three-digit SIC code. Dasgupta,2019 shows how to match these two datasets: ...
-2
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0answers
40 views

Why is variance of brownian geometric motion equal to t? [closed]

I know that, for the random variable $B_t$, $B_t \sim N(0, t) = X\sqrt{t}$ where $X \sim N(0,1)$. However, what I am confused by is why the variance of the GBM variable is assumed to be $t$ in the ...
0
votes
1answer
105 views

Why does the rate of inflation vary over time?

Interest rates have varied significantly over the last 50+ years (source: https://www.macrotrends.net/2016/10-year-treasury-bond-rate-yield-chart ). Is it possible to comprehensively and succinctly ...
1
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0answers
72 views

Black-Scholes with two options

I have got a Black-Scholes model with portoflio with two options which bond prices are $V_1$ and $V_2$ (with different maturities or strikes). The interest rate $r$ is stochastic and given by: $$ dr = ...
1
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0answers
16 views

Checking Regression Inputs & Outputs (Factor Regression)

I am looking to check the assumptions and interpretation of the output of a regression that I have run for factor exposures in a long/short equity portfolio: Portfolio is long/short equity with a net ...
-2
votes
1answer
37 views

One-Period Binomial Model

So, I'm required to consider the one-period Binomial market model for a particular question. We're told that the savings account is \$1 at time 0 and \$β at time 1. The stock price is given by S0 = 1 ...
0
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0answers
18 views

Interpretation of holding lower beta assets leveraged to a beta of one and short high beta de-leveraged to a beta of one

I was reading the famous paper "Betting against Beta" by Frazzini et al. They created BAB factor in which a portfolio is created by holding low beta assets, leveraged to a beta of one" ...
0
votes
1answer
52 views

Covariance Shrinkage - Am I getting the right variances?

I am looking into a quite simple task: shrinking the sample covariance matrix of a minor sample of monthly returns data on 5 different assets. I am using Python to process my data and have been using ...
4
votes
2answers
119 views

Conditional expectation of integral of brownian motion

I am trying to calculate $$\mathbb{E}\biggl[\biggl(\int_s^t W_u du\biggl)^2 \biggl|W_s=x, W_t=y\biggl] $$ where $W$ is a Standard Brownian Motion and $s\leq u \leq t$. Any help or tips would be ...
0
votes
0answers
34 views

Monte carlo simulations giving biased output

I wrote code to simulate the stock price using geometric brownian motion. My code is as follows: ...
1
vote
0answers
26 views

Calculating E^2[σ^2] where σ is a GARCH(1,1) Proces

Given that α =0,113079 β = 0,873884 ω = 0,0000081 Need the calculate a call price using garch volatility I alsa calculated the kurtosis = 235 enter image description here: https://www.researchgate.net/...
3
votes
1answer
50 views

EMM for Bachelier model

The stock price is assumed to evolve as $S_{t}=S_{0}+\mu t+\sigma B_{t}$, where $S_{0}>0, \mu>0$ and the process $B_{t}$ is Brownian motion. The saving account is assumed to be $\beta_{t}=e^{r t}...
1
vote
1answer
64 views

R - Plotting a 3-dimensional sample path in yuima?

Apologies if this is not the appropriate place to post this - this my very first contribution to Quantitative Finance Stack Exchange. I was hoping someone could help me with the following issue. I am ...
0
votes
1answer
24 views

How to set up the industry-level variables in an international study based on North America data?

In some international studies, authors usually use the industry-level in North America (US and Canada) to control for all-even non-North American-countries. I am quite confused about how to do that in ...
0
votes
0answers
24 views

Python Libraries for candle stick analysis

I'm a complete newbie to technical analysis so please forgive the rookie question. I'm looking for python libraries that can classify different types of candle sticks and maybe even provide some ...
1
vote
1answer
27 views

Replicating Portfolio / Complete Market / Attainable Claim

Attempt So Far: 1) First Part: I have shown that the market is arbitrage-free since the only possible portfolio for which $V_1^h\geq0 \ $ given that $V_0^h=0 \ $ is $h=(0,0,0)$ and this clearly ...
2
votes
1answer
56 views

Feynman-Kac representation of Black-Cox model

Consider the standard setup from Black and Cox (1976, Journal of Finance). A firm issues a defaultable coupon bond to finance a productive asset that follows a geometric brownian motion: $$dx_t = \mu ...
0
votes
0answers
53 views

Optimise the Sharpe ratio of a portfolio of uncorrelated assets

Given a portfolio of $n$ assets, mean returns vector $\mu$, covariance matrix $K$, one can calculate the portfolio weights $w^*$ that maximise the portfolio Sharpe ratio, by solving: $$w^*=\text{...

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