All Questions
22,174
questions
2
votes
0
answers
43
views
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 ...
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 ...
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 ...
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% ...
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 ...
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.
...
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 ...
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 ...
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 ...
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/...
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 ...
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 ...
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 ...
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 ...
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
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 ...
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 - ...
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 - ...
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.
...
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 ...
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 ...
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 ...
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 ...
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 ...
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, ...
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 ...
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 ...
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 ...
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 ...
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:
...
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
$$
For_S(t,T) = \frac{S(...
3
votes
2
answers
708
views
Average drawdown and average drawdown length in Python
I'm trying to use Python to give me more information about drawdowns than just the max drawdown and the duration of the max drawdown. I would like to determine the number of drawdowns that have ...
3
votes
1
answer
190
views
Which volatility measure would you use for intraday minute data?
I have a very detailed dataset - for each minute I can see 3 best bid and ask prices with associated quantities. Which measure of volatility would you use in such dataset? Some volatility measures use ...
0
votes
1
answer
198
views
Is American put Gamma always greater than the European one in the non-early-exercise domain?
Consider a pair of American and European puts with the same specifications except the former has the continuous early exercise right. Has anyone plotted the Gamma's of both as functions of the ...
3
votes
1
answer
473
views
Mixing Max Drawdown and Sharpe Ratio in a single utility function : is there a standard approach?
We know that 2 strategies can give the same Sharpe Ratio, but with different Maximum Drawdown. I computed myself these 2 strategies having the same cumulative return and SR, but with considerably ...
5
votes
1
answer
203
views
Quantlib Slow valuation of ois_swap on multiple eval days
I have bootstrapped a curve using several depo and swap rates and am trying to use that curve to get the NPV of a swap over a period of time. The generation of prices iteratively through time is ...
2
votes
0
answers
148
views
Bond-pricing under the Vasicek short rate model
I'm currently studying the Vasicek model of the short interest rate
$$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 ...
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 ...
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 ...
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....
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.
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 ...
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 ...
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 ...
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 ...
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 ...
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 ...
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 ...
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 ...
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?
...