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Pricing equation with two correlated states

Consider the following asset pricing setting for a perpetual defaultable coupon bond with price $P(V,c)$, where $V$ is the value of the underlying asset and $c$ is a poisson payment that occurs with ...
Luca Gi's user avatar
  • 327
0 votes
0 answers
27 views

How to find stock i’s benchmark return for Cash-Value Regression

I would appreciate any help or guidance please as I do not understand how to find the corresponding portfolio to use as benchmark to find the Excess Return that is used in the Baseline Regression ...
JoseMM's user avatar
  • 13
1 vote
0 answers
73 views

Optimal exercise time in Binomial model

Let (B, S) a multi period binomial model that is arbitrage free. I would like to prove that the unique optimal exercise time for an American call option is the maturity time T. My idea is to prove ...
user avatar
3 votes
2 answers
334 views

Maximum profit from trading on a random walk with a specific strategy

My question is related to this thread, but I'm interested in a special case. Suppose that the price of an asset starts at 100 USD, and changes according to a geometric random walk; one step of 1% ...
asmani's user avatar
  • 141
1 vote
1 answer
215 views

Figuring out how TradingView calculates the Sharpe ratio [closed]

This is the simplest backtest I've come up with, yet I can't figure out how TradingView has calculated the Sharpe ratio to be 0.577. I've set the risk_free_rate=0. Is it possible to extract the ...
asmani's user avatar
  • 141
4 votes
1 answer
165 views

Quadratic Variation Of Mixed Brownian Motion and Poisson Process

I am trying to solve this problem where we're asked to compute the quadratic variation of a process. I assume that it is necessary to apply Ito's formula but not sure how to get the right solution. ...
Niko's user avatar
  • 43
0 votes
0 answers
59 views

What is the correct way to think about volatility - in raw terms or logs?

I'm thinking about the relationship between the volatility of a bunch of single stocks and the US VIX - as the companies in question tend to export heavily to the US. To get a grasp over the beta ...
Student's user avatar
  • 151
3 votes
0 answers
42 views

Active risk management of private assets

It seems incredibly difficult to not only come up with a list of options for active risk of private assets (Private Equity, Private Credit, Infrastructure, Real Estate, etc.) but also get senior ...
AK88's user avatar
  • 1,840
1 vote
1 answer
178 views

Is there a risk-neutral measure if there are two stocks with different drift terms?

There are two stocks: $S_t$ and $P_t$ $$dS_t = S_t(\mu dt + \sigma dB_t)$$ $$dP_t = P_t((\mu + \varepsilon) dt + \sigma dB_t)$$ Is there any risk-neutral measure? My thoughts are pretty simple: $μ$ is ...
nearhome's user avatar
0 votes
0 answers
43 views

Origin of the formula Varswap strike $= \int_{\mathbb R} I^2(d_2) n(d_2)\, \mathrm d d_2$

As stated in the title, who first derived the formula $$ \text{Varswap strike} = \int_{\mathbb R} I^2(d_2) n(d_2) \, \mathrm d d_2 $$ where $d_2$ is the Black-Scholes quantity $$ d_2 = \frac{ \log S_t/...
Frido's user avatar
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0 votes
0 answers
68 views

Hedging of FX combo trade

Say we’re selling a TRS on a local MSCI index denominated in USD and delta hedge it by buying eq futures on that local index denominated in local currency (non USD). Let’s also ignore repo/div/ir risk ...
Jamesr's user avatar
  • 23
0 votes
0 answers
62 views

Does Backtrader and QuantConnect collect any data?

Building an API that integrates with backtrader and QuantConnect to run some backtests. I'm passing in machine generated data and I just want to make sure I'm not sending them too much stuff. so what ...
keon6's user avatar
  • 61
0 votes
0 answers
80 views

LSMC for Out of The Money paths

In the Longstaff & Schawartz article they condition on using In-The-Money (ITM) paths only for the regression. The reason for this is to obtain more accurate results and also reduce the ...
Landscape's user avatar
  • 558
1 vote
1 answer
368 views

XCS and FX swaps: market risks

XCS (cross currency swap) can be: Float vs float #1 Fixed vs fixed #2 Float vs fixed #3 #2 can be constructed with 2 fixed vs float irs and 1 xccy basis swap #1 #3 can be constructed with 1 irs and ...
Jamesr's user avatar
  • 23
2 votes
0 answers
82 views

Closed form solution to get implied vol from delta with SABR model

Given a set of calibrated SABR parameters, what is the approach to get the implied vol for a given delta ? thanks
zotson's user avatar
  • 21
1 vote
0 answers
77 views

Black Litterman Model: can Market Weights be replaced?

I'm new to applying the Black Litterman model. One point that is troubling me, from a multi asset point of view, is the market portfolio as the starting point for the model. Correct me if I'm wrong ...
Farrep7's user avatar
  • 11
2 votes
0 answers
114 views

multivariate geometric brownian motion equivalent martingale measure

Suppose $W$ is a $\mathbb{P}$-Brownian motion and the process $S$ follows a geometric $\mathbb{P}$-Brownian motion model with respect to $W$. $S$ is given by \begin{equation} dS(t) = S(t)\big((\mu - ...
yrual's user avatar
  • 151
5 votes
0 answers
223 views

Black-Scholes formula is a (probabilistic) convex combination

A call price is bounded when $\sigma\sqrt{T}$ goes to $0$ and $\infty $ by: $$C_{inf} = e^{-rT}[F-K] \leq C \leq C_{sup}=S $$ Now a simple rearrangement of Black-Scholes formula gives: $$ C = N_1S - ...
bigInner's user avatar
  • 191
6 votes
1 answer
245 views

Why do we use the letter $q$ for dividends?

In derivative pricing models, we often use the letter $q$ to designate the dividend yield i.e.: $$\textrm{d}S_t=S_t((\mu-q) \textrm{d}t+\sigma\textrm{d}W_t)$$ for the price process $S$ of the stock. ...
Daneel Olivaw's user avatar
1 vote
0 answers
108 views

Calibration of LSV models to vanna/volga break-even

In this paper, Labordère, the author computes a probabilistic representation of the the vanna/vomma(volga) break-even levels. He mentions that they can be used to calibrate LSV models to historical ...
Greyearl's user avatar
1 vote
0 answers
216 views

SabrSwaptionVolCube Class in Quantilib Python

Just noticed after upgrading to the most recent version of Quantlib Python that the class ql.SabrSwaptionVolCube is now available. This is a very useful class in that it behaves in very much the same ...
user35980's user avatar
  • 1,386
0 votes
0 answers
109 views

Is it okay to fetch market data from platform A and trade on platform B? (Forex)

I am currently trading forex on capital.com but since they don't offer tick data I am considering to fetch the tick data from polygon.io and then trade on capital.com. Though I am wondering if this is ...
user7934593's user avatar
3 votes
0 answers
103 views

Using CAPM to find the price of an option

I was reading a textbook about finding the price of an option on a one-period binomial model. The textbook way of doing it is to replicate the option with cash and stock for $t=T$, and then calculate ...
Mango's user avatar
  • 31
5 votes
0 answers
112 views

Portfolio immunization in time

The company will have to pay out an amount of liabilities $13594$ at the moment $t=9$. In $t=0$ they want to cover it with 4-years zero-coupon bonds and yearly perpetual annuity that is due in arrears ...
Miłosz 's user avatar
1 vote
1 answer
125 views

Confusion about the formula for gain process in a financial market

In this wikipedia page, we consider the following financial market The formulas for the stocks are given here And the gain process of a portfolio $\pi$ is defined such that From what I understand, ...
yrual's user avatar
  • 151
3 votes
0 answers
77 views

Methods for tracking option open interest intraday

It is my understanding that open interest option values on financial websites are a reflection of a snapshot value each day. Is anyone aware of methods for estimating intraday open interest, or aware ...
skepticalforever's user avatar
0 votes
0 answers
34 views

Risk Neutral Pricing - Why the Risk Free rate for Risky security (Intuition) [duplicate]

I am struggling with this concept of risk neutral probabilities. My understanding of how a risk neutral pricing framework works is as follows: (discrete, binomial lattice for simplicity) I do not know ...
Jaimeblt1's user avatar
0 votes
1 answer
52 views

Non-stationarity and repricing as a source of idiosyncratic and systematic "risk"?

1.Assuming a one period economy with two assets in which cash flows are assigned certain probabilities, using the CAPM, we can derive the P0 given the E(CF) at t1. Within this distribution, we have ...
Leonid Konoplev's user avatar
2 votes
0 answers
75 views

PTP 10% Withholding [closed]

Apparently there's a new IRS rule that can be summarized as "starting January 1st, 2023, investors who are not U.S. taxpayers must withhold 10% of proceeds from the sale of PTPs (Publicly Traded ...
Gabi's user avatar
  • 131
2 votes
2 answers
747 views

Quantlib SOFR swap repricing across 2 different dates

I am trying to price SOFR swaps in two different dates (the same swaps, just different curves and dates) This are my initial parameters: ...
Lucas Triana's user avatar
0 votes
0 answers
68 views

No arbitrage argument for the price process of a forward contract

I was reading the book Stochastic Calculus for Finance II by Shreve and I read the proof that the forward price for the underlying $S$ at time $t$ with maturity $T$ is given by $$ For_S(t,T) = \frac{S(...
julian2000P's user avatar
3 votes
2 answers
708 views

Average drawdown and average drawdown length in Python

I'm trying to use Python to give me more information about drawdowns than just the max drawdown and the duration of the max drawdown. I would like to determine the number of drawdowns that have ...
user89135's user avatar
  • 304
3 votes
1 answer
190 views

Which volatility measure would you use for intraday minute data?

I have a very detailed dataset - for each minute I can see 3 best bid and ask prices with associated quantities. Which measure of volatility would you use in such dataset? Some volatility measures use ...
Avocado's user avatar
  • 45
0 votes
1 answer
198 views

Is American put Gamma always greater than the European one in the non-early-exercise domain?

Consider a pair of American and European puts with the same specifications except the former has the continuous early exercise right. Has anyone plotted the Gamma's of both as functions of the ...
Hans's user avatar
  • 2,806
3 votes
1 answer
473 views

Mixing Max Drawdown and Sharpe Ratio in a single utility function : is there a standard approach?

We know that 2 strategies can give the same Sharpe Ratio, but with different Maximum Drawdown. I computed myself these 2 strategies having the same cumulative return and SR, but with considerably ...
Jerem Lachkar's user avatar
5 votes
1 answer
203 views

Quantlib Slow valuation of ois_swap on multiple eval days

I have bootstrapped a curve using several depo and swap rates and am trying to use that curve to get the NPV of a swap over a period of time. The generation of prices iteratively through time is ...
StormsEdge's user avatar
2 votes
0 answers
148 views

Bond-pricing under the Vasicek short rate model

I'm currently studying the Vasicek model of the short interest rate $$dr_t=a(\mu-r_t)dt+\sigma dW_t$$ I know how to solve this stochastic differential equation (SDE) and how to find expectation and ...
Don Abbondio's user avatar
1 vote
0 answers
52 views

Market risk in Tier 1 capital of a bank

The common stock of the bank is considered to be a part of the Tier 1 capital, but it is also subject to market risk. The Investopedia definition distinguishes between Tier 1 and Tier 3 capital by the ...
cookiemonster's user avatar
2 votes
0 answers
54 views

Black's formula derivation: expectation of a indicator times a random variable

In this derivation of Black's formula for puts, we have that $\mathbb{E}[e^X 1_{e^X \leq K/S_0}]$ somehow equals $S_0 e^{\mu + 0.5 \sigma^2} N$ (as above in the formula). I tried breaking apart the ...
Jerry Qu's user avatar
1 vote
0 answers
94 views

From model vega matrix to market vega matrix

I'm reading Antonie Savine's fascinating book Modern Computational Finance AAD and Parallel Simulations. However, I got a bit confused while reading and couldn't make sense of how it works in his work....
James's user avatar
  • 11
2 votes
0 answers
38 views

Finding upper bound for portfolio made from European call / put options

I tried finding upper bounds for each component in terms of E_1 using the put call parity but couldn’t get the correct answer.
Alex Seitzy's user avatar
2 votes
1 answer
110 views

Fatigue with Historic Backtesting - Alternatives?

It seems to me like historic backtesting is the best of bad options out there for me to test my systematic strategies - even ones that are more macro-level trend spotting. I can't test enough ...
keon6's user avatar
  • 61
2 votes
0 answers
73 views

Optimal portfolio as combination of target and minimum tracking error portfolios?

Dear Quant StackExchange I seek some intuition for how my portfolio behaves given constraints. In a universe of say 5 assets, I have a "target portfolio" with weights that are found from ...
fdp1996's user avatar
  • 21
5 votes
1 answer
257 views

What color financial time series are there?

There is a folklore white noise hypothesis related to (and equivalent to some forms of) the efficient market hypothesis in finance -see references below. But are there some asset pairs whose return ...
plm's user avatar
  • 151
8 votes
1 answer
675 views

Option time value is Nd1-Nd2

I can't find the below statement anywhere (rearrangement of Black-Scholes formula) : $C(0, S) = e^{-rT}N_2[F-K] + [N_1-N_2]S$ $F$ being the forward, it reads as a straightforward decomposition to ...
bigInner's user avatar
  • 191
3 votes
0 answers
119 views

Methods to estimate Options volume

I need to build a Liquidity Risk report at my intern job. There, I consider an MDTV90 (Median Daily Traded Value for 90 days, a measure of liquidity) for each asset we trade to find how many days we ...
Fróis's user avatar
  • 31
3 votes
1 answer
368 views

Proper way to backtest strategy using bootstrap method

Should I back-test in a single (original) price series and bootstrap the strategy returns to get statistics of interest? Or should I create bootstrapped price series using bootstrapped returns from ...
Arun Lama's user avatar
3 votes
0 answers
57 views

Dynamics of independent Geometric Brownian Motions under risk-neutral measure Q

Suppose I have two Geometric Brownian motions and a bank account: $$dB_t=rB_tdt$$ $$ dS=S(\alpha dt + \sigma dW_t) $$ $$ dY = Y(\beta dt + \delta dV_t) $$ Where $dW_t$ and $dV_t$ are independent ...
zjo892's user avatar
  • 31
0 votes
0 answers
47 views

Understanding the adjustment $(u/r) p$ in the binomial options pricing formula

I'm reading Option Pricing: A Simplified Approach and have a question. Assume the binomial tree model for the stock. So $n$ discrete time periods $S$ is stock $C$ is call $K$ is strike $u$ is upward ...
jds's user avatar
  • 138
1 vote
2 answers
120 views

Why do we need an ex-dividend date? [closed]

Why do we need an ex-dividend date? What is the problem with the ex-dividend date being the same as the payment date? Why are they separate? What problem does having a separate ex-dividend date solve? ...
s5s's user avatar
  • 452

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