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5 views

Applying GRS-test on non-normal residuals with autocorrelation

Is it valid to apply GRS-test (Gibbons, Ross and Shanken 1989) on non-normal and autocorrelated residuals? I got residuals using 10 test-assets regressed on 3-factor and carhart. If it is valid, how ...
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0answers
7 views

Representing relative stock price predictions in portfolio optimization

I wanted to ask a simple question in representing mathematical concepts/terms into the portfolio optimization utility functions. I have never worked with these in production environment so I am very ...
0
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0answers
12 views

Hedging Using Zero Coupon Bonds in an Arbitrage Free Pricing Forex Problem

I'm reading Mark Joshi's Concepts and Practice of Mathematical Finance, where in section 2.5 he describes an example of arbitrage-free pricing (attached below). I have a pretty solid understanding of ...
-4
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0answers
29 views

Meta-Question: Why do a lot of people in quantitative finance get in trouble? [closed]

I'm trying to understand the causal factors here. It seems on general, people in finance get into trouble with the law. Whereas people in tech don't get into as much trouble. What's up with that?
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0answers
15 views

complete python code to calculate risk neutral density from option prices

bAsic python code to implement Litzenberger formula for risk-neutral probabilities implied by option prices. Use S&P 500 option prices whose strike intervals are typically 5 points apart use at ...
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2answers
34 views

Value of a 30 year bond using the Yield curve

If I buy a $1 30 year bond with 4% coupon payment, would my cash flow be: $$ V^{30}(t) = \frac{$1 \times0.04}{1 + R(t, 1)} + \frac{$1 \times0.04}{1 + R(t, 2)} + \cdots + \frac{$1 + $1 \times0.04}{1 + ...
1
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1answer
29 views

Canonical text on numerical PDEs in finance

I am looking for a text similar to Glasserman's Monte Carlo Methods in Financial Engineering, but with a focus on numerical methods for PDEs. Glasserman's book seems to cover a lot for what is ...
0
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2answers
36 views

Stochastic Volatility Models - are they complete markets?

I'm reading about stochastic volatility models - the ones which resulted after Wiggins proposed in 1986/7 that $\sigma$ in Black-Scholes should be a stochastic process rather than a constant. In ...
-3
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0answers
28 views

dB=rBdt: express B(T) in terms of B(t)

Consider a risk free asset with continuously compounded return of r. Let $B$ be value invested in the asset. $dB=rBdt$: write the expression for $B(T)$ in terms of $B(t)$
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0answers
19 views

Futures vs Forward pricing with different interest rates using binomial model

I'm given the aforementioned parameters for a two-step binomial model where the underlying pays no dividend, $S_0=50$ and $T=2$. With this information I was able to calculate the risk-neutral ...
0
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1answer
36 views

Is the forward price equal to the future price?

If $f^{T_1}(t)$ is the price of a forward and $F^{T_1}(t)$ is the price of a future on some stock, both maturing at date $T_1$ and with the assumptions: no dividend constant interest rates no ...
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0answers
21 views

How to understand “the world defined by specific numeraire”?

I am reading John Hull's book. When talking about "equivalent martingale measure result", the author introduces the concept of "the world defined by specific numeraire g" to describe the world in ...
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0answers
21 views

Compare the perfomance [closed]

Sara has graduated with a Finance diploma with an average of 72, where the averages of the finance students are normally distributed with a variance of 49 and a mean of 63. - Mark has graduated with a ...
-3
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0answers
24 views

Best option to buy? Explain your answer [closed]

Options A & B sell for \$5, for an underlying stock which currently sells at \$30. Both mature in 1yr, & risk free rate=6%, variance=30%. Upon maturity, exercise option A for \$25, and option ...
0
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1answer
40 views

Do I have to annualize daily volatility?

my question may be very dumb but I computed daily returns as the log(Pt)-log(Pt-1) in order to get the volatility. But I do not want to present my results over a certain period of time (whether it's a ...
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0answers
19 views

Get the weights of porfolio variance given standard deviation

I am trying to create a Simulated Portfolio Optimization based on Efficient Frontier on 50 stocks, which you can find the csv here. Yet it already takes me several minutes to get a suboptimal solution:...
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0answers
42 views

Vega hedging swaption with caplets - precisely, what will go wrong?

I am trying to form a kind of unified perspective of how (vega) hedging an exotic with vanillas, or hedging a 'basket option' with vanillas will go wrong. So in particular, I want to be able to ...
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0answers
34 views

Cross hedge: Which commodity to hedge when you have to hedge the jet fuel price but you have option between two commodities

If we have an option between two commodities to hedge jet fuel and the commodities have results as follows: minimum variance hedge ratio: 1.07 for commodity 1 and 2.53 for commodity 2 ...
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4answers
145 views

Quantitative finance for physicists

I am looking for good books to learn quantitative finance. As I have strong background in physics, I would appreciate introductions that do not hesitate to show the equations, but in the same time ...
4
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0answers
81 views

Black-Scholes market and payoff with integrals

I am struggling with the following exercise: Prove that on Black-Scholes market, with some parameters $r, \mu, \sigma >0$, a payoff $$X=\int_{0}^{T}\ln \frac{S_t}{S_0}\mathrm{d}t+\frac{1}{\...
2
votes
1answer
57 views

Can a portfolio value consisting of longing a delta shares of stocks and shorting a call option greater than strike price?

While trying to implement Black-Scholes delta hedging for a European call option using Python, I came across the following phenomena: Given a portfolio consisting of longing a delta shares of ...
0
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1answer
37 views

Is “time value of currency” to be accounted for in returns calculation?

A simple question: When exchanging currency in order to finance an investment, is it standard/best practice to adjusted for exchange rates when calculating the NPL of that investment? For example: I, ...
2
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2answers
55 views

Quantlib: convert par swap rates to zero rates back and forth

I built a zero-coupon curve out of a generic par swap rate curve (Step 1) and I am trying to recover the swap curve back from the zero-coupon curve (Step 2). Step 1 works but not Step 2. I get close ...
2
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0answers
20 views

Far OTM calculation issue on Bjerksund-Stensland

Has anyone come across and fixed calculation issues on boundaries using Bjerksund-Stensland 2002 (Hull, Haug or Rouah implementations) ? Thanks in advance
0
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1answer
29 views

Net volume reference for uptick and downtick

I am new to finance and I have been looking at market data in terms of prices, volumes and net volumes. From what I have gathered: Volume - number of transactions (buying-selling) throughout the ...
0
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0answers
29 views

Discreet-time stochastic difference equation and Ito thorem

In continuous time, when we want to find the dynamics of a function of a stochastic process, we need to use Ito's lemma which gives an "extra"" term for the drift. What if we are in discreet time and ...
0
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0answers
8 views

Volume bars, dollar bars from low-frequency data?

Financial models by default use time bars for input data. I use time bars to refer to both intraday (high frequency) and interday (low frequency data) since the sampling occurs at fixed intervals of ...
0
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2answers
43 views

Which Nikkei225 futures contract to take?

I have a working (swing) trading strategy based on equity index futures in place. I enter and exit by giving market orders. The strategy generates roughly 40 trades per instrument per year. I want to ...
0
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1answer
34 views

Portfolio optimization with multivariate returns of different length

The mean variance model of Markowitz that uses multivariate covariance matrix requires the length of each of the N assets return time series under consideration to be of equal length. Are there any ...
0
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0answers
40 views

How do you formulate trading ideas and strategies?

I have access to some tick data and Bloomberg data. Outside of data mining and hoping to find an economic rationale after the fact, what do you usually do to generate ideas before you look at the ...
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0answers
27 views

why do we need to exercise perpetual call option immediately if stock price $S$ is over the optimal price $H_1$?

In Section 26.2 "perpetual American call and put options" of John Hull's "Options, Futures, and other Derivatives", the author mentioned that there is an optimal stock price $S=H_1$ where perpetual ...
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0answers
22 views

why does “one-shot derivative” boundary condition hold for perpetual American call options?

When reading John Hull's book about perpetual options (Section 26.2: "perpetual American call and put options", 10th edition), I am a bit confused about the boundary conditions used here. The author ...
1
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0answers
33 views

Trying to measure “radius of diffusion” in the stock market

Good evening! I'm quite new to quantitative finance (coming from the math world!), so please excuse me if I'm not familiar with every concept! I am currently studying the Black-Scholes equation, ...
0
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1answer
46 views

Which one is the optimal risky portfolio in the efficiency frontier in the absense of a risk free asset?

I know that the tangency point between the CAL line (drawn from risk-free asset's return) and the efficiency frontier is the optimal risky portfolio. But what if there is no risk free asset? Can I ...
0
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1answer
46 views

How can I theoretically hedge a bet, which is about whether or not price of a stock will get above a number?

For example, the bet may be about someone giving me P dollar and I will pay that person 300 dollars if tomorrow Tesla gets above 860 dollars. While assuming the Black-Scholes model hold, I can simply ...
0
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0answers
36 views

Martingale optimal transport

I'm a student and currently studying martingale optimal transport for deriving upper and lower contract bounds but i happen struggling on the fact that in most papers , interest rates are not taken in ...
2
votes
1answer
83 views

Simple strategies for tail risk hedging that retail investors can use

Universa Investments run by Mark Spitznagel popularized the idea of portfolio insurance (also known as tail hedge) protecting the investor against severe market declines (tail risks). By using this ...
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0answers
36 views

Why are cashflows “modelled backwards in time”?

A am currently reading a manual on how to use some actuarial modelling software to project the expected liability payments made under an annuity contract. In this guide, the following statement is ...
-3
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0answers
23 views

Pdshare in multivariate

How to calculate price discovery components information share and component share using pdshare for three instruement as we know pdshare designed for bivariate. But I am looking for pdshare in ...
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0answers
29 views

How to build the 3 month LIBOR Forward curve through Swaps?

In my research, I found that you can build 3 month LIBOR Forward curve using Eurodollar futures and Interest rate swaps. I want to understand how they can be built from Swaps. How can I find the ...
1
vote
1answer
40 views

Do you need to simulate the entire stock path for option pricing with GARCH?

I'm trying to price European options with a GARCH volatility model. What I have is a program that calibrates the GARCH volatility process for a stock which I intend to use to value a derivative on the ...
0
votes
0answers
24 views

How to build the Fed Funds Rate which is a discounting curve? Need this information for modelling the SOFR curve

I want to understand how one could construct the Fed Funds rate. I read somewhere that this could be done using fed funds futures but I wasn't able to understand how Can someone elaborately explain in ...
0
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0answers
37 views

The definitions of swap's dv01, annuity, analytic delta [closed]

I have seen the various definitions of the three concepts. Are they essentially the same thing.
1
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0answers
45 views

Does simulating price as GBM automatically implies risk neutrality?

I am using a dynamic programming approach to price European options where formulate the pricing as a discrete-time continuous-space Markov Decision process. The MDP is risk-sensitive as in I don’t ...
0
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0answers
35 views

Hedging Bond portfolio with Futures

I am working on a risk department. Our portfolio contains mostly some long German bond 15y and we tend to hedge it through BUXL and BOBL via PCA but our 15y key rate duration is not properly covered. ...
1
vote
0answers
38 views

Constructing a Beta Neutral Hedge in a Pairs Strategy

Looking for resources / explanation. Creating a dollar neutral hedge is easy - stockprice-a/stockprice-b How do I create a beta neutral hedge? I find discussions but no explicit derivation ...
0
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0answers
48 views

Bond Options Calibration to market volatility using SABR Model

I'm trying to calibrate bond option implied volatility from SABR model to market volatilities, I tried calibration in python but the smile isn't correctly matching with market volatility? Any help is ...
1
vote
0answers
97 views

Dynamic programming and Bellman equation to obtain the maximum

This is the problem of Marhsall (1992) "Inflation and Asset Returns in a Monetary Economy" and Balvers and Huang (2009) "Money and the C-CAPM" Suppose an endowment economy where the representative ...
1
vote
3answers
109 views

CAPM and Beta: problem with regression (Beta is too low yet statistically significant?)

I have two time series of daily return calculated as $\frac{Price_{t}}{Price_{t-1}} -1$. One is the daily returns of a portfolio, the other the daily returns of the index (MSCI World). Period is 2020 ...
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0answers
28 views

How do you solve this question? [closed]

How do I solve this? Is there a direct method?

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