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11 views

Link between spot and forward rates in no-arbitrage world

With reference to the forward exchange rate definition, let be: $S$: the spot rate $F$: the forward rate $r_d$ and $r_f$: respectively the domestic and foreign interest rates $DF_d$ and $DF_f$: ...
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0answers
4 views

Relationship between Data Size and Arima Prediction Interval Width?

When we use Arima model to acquire Interval Predictions, will the width of prediction intervals decrease if we use more data (longer history) to fit the model?
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2answers
34 views

How to show if this is Martingale or not?

Consider the outcome of a game played by repeatedly tossing a fair coin, where you win a dollar if heads appears and you lose a dollar if tails appear, the outcome is denoted 𝑋1, 𝑋2,𝑋3, … . . 𝑋𝑛. ...
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1answer
14 views

MonteCarlo option pricing error estimate

Consider the problem of pricing an option via MonteCarlo with 10000 simulations. If the variance of the simulation is 100, which is the MC estimate of the error on the price?
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0answers
16 views

Why is it not a markov process, but a martingale process?

I understand how the n+1 outcome depends on nth outcome, and nth outcome depends on n-1, but how to show it?
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0answers
12 views

Updated Time Series Prediction Model When acquiring new data Points - Basic Question

Suppose I have a Time Series Model (assume ARIMA) and use it to make one-step ahead prediction. If I acquire a new data point, (for example I was originally using the first 100 days to fit an Arima ...
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2answers
26 views

How do we determine the “correct measure”?

Frequently I come across the statement that the "correct measure" for a product is this-or-that measure. For example, Eurodollar Futures or Stock returns - Risk neutral measure Libor forward rate - T-...
0
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1answer
23 views

How do we derive the Radon-Nikodym derivative for T-forward measures?

Let $Q^{T_e}$ denote the $T_e$-forward measure and let $Q^{T_p}$ denote the $T_p$-forward measure. I have seen the following Radon-Nikodym derivative being used in derivations. For $0 \le t \le T_p$, ...
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0answers
12 views

What is the continuous time approx formula for the par yield curve?

I understand that the par rate is the single discount rate that you would use to discount all of the bond’s cash flows to get today’s market price. I also see that assuming a spot rate function $R(t)...
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1answer
29 views

Cross Currency Swap - is par basis supposed to change while OIS discounting rate is changing?

Assume a USDJPY cross currency basis swap priced using usd ois & usdjpy basis curve as discounting, and usd libor & jpy libor as projection curve. Now if usd ois is moving in the market while ...
9
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3answers
6k views

Where can I find a list of VaR and CVaR formulas for continuous distributions?

Where can I find more VaR and CVaR formulas for continuous distributions? I collected a list here:
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1answer
52 views

Why does a Bermudan option have a higher implied volatility than its European counterpart?

I get that the premium for an earlier exercise should be higher to compensate the seller but intuitively you would think that the spot has "less room to run" in a potentially shorter period of time (...
1
vote
1answer
9k views

Margin % Bridge - Effect of Price, Cost, Volume

Given sales and profitability data for two time periods, how would I go about calculating the impact of price, cost, volume and mix margin % (bps)? I can do the analysis as a gross margin $ bridge, ...
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0answers
25 views

Downloading all stocks of an index from CRSP

I am new to the CRSP database and wanted to ask if it's possible to download all the stock prices/returns (daily or weekly) of e.g. the NASDAQ Index (just like in Bloomberg)? And if yes, how exactly? ...
0
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1answer
76 views

Derivation of Swap rate formula

Assuming usual notation, I derive the floating rate and fixed rate payoffs and set them equal. The par swap rate I get thus is: $$S_{mn}\mid_{t=0} = {\sum_{i=m}^{N-1} \tau_i L(0, T_{i-1}, T_i)Z_{0i} \...
4
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0answers
29 views

Relating two equations in a jump-diffusion process

I am trying to understand an argument involving the pricing kernel $\xi_t$ in the context of a simple jump diffusion model for the price of an asset $S_t$: \begin{align} \xi_t = \exp \left[ -\theta ...
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1answer
127 views

Predicting time series using Jump Diffusion model and Neural Networks

I am trying to understand the difference between using Jump diffusion model and Neural Networks or more precisely LSTM to predict time series data regardless what that data contains for example a ...
1
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1answer
96 views

How to gamma hedge and vega hedge an autocallable product?

I am pretty new in quantitative finance, and I am interested by the hedging of autocalls. Could you, please explain which financial products should be traded (specify the way, please) to delta hedge, ...
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0answers
35 views

Duration of forward starting swap

For a spot starting interest rate swap, the duration is calculated as the duration of the fixed rate leg less the duration of the floating leg. Each of these calculations is akin to calculating the ...
1
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1answer
78 views

Going from $\mathcal{P}$ to $\mathcal{Q}$

Under $\mathcal{P}$, we have the Heston Model given by: $$ d S_{t}=\mu S_{t} d t+\sqrt{\nu_{t}} S_{t} d W_{t}^{S},\\ d \nu_{t}=\kappa\left(\theta-\nu_{t}\right) d t+\xi \sqrt{\nu_{t}} d W_{t}^{\nu}. $...
1
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1answer
74 views

Which method is used to price highly exotic options in exotic models?

What is the go-to method to price exotic options in exotic models? If we are in Black Scholes, then this is hard to answer, since we can both do various sorts of Monte Carlo or solve various sorts of ...
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0answers
34 views

Vol surface fitting with 5 degrees of freedom

For an options market making operation I need to be able to build a volatility surface, based on only 5 degrees of freedom, like e.g.: MaxPut, MaxCall, Skew, Curve and At The Money Vol. Is there an ...
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0answers
64 views

Swaps: What is the difference between Outright and Spread trading?

I understand in Swaps there are two investing strategies called Outrights and Spreads. Could someone please confirm my understanding of them? I understand an Outright strategy in Swaps refers to ...
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0answers
18 views

Strict stationarity of GARCH(1,1) process

Consider the following GARCH(1,1) process: $$ \epsilon_t = \sigma_t \eta_t \quad \text{where} \quad (\eta_t) \overset{iid}{\sim} \mathcal{N} (0,1)$$ $$ \sigma_t^2 = \omega + \alpha \epsilon_{t-1}^2 + \...
1
vote
1answer
64 views

PDs for negative credit spreads

My question is about credit spreads and the corresponding probability of default (PD). One of the most simple relations between credit spreads and PDs is (see e.g. ch7 in Malz(2011)) $$ PD \approx \...
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1answer
74 views

Calculate return for a set of securities downloaded using quantmod

I downloaded adjusted closing price using quantmod for a set of securities. I want to calculate daily/weekly/monthly return for all securities. Usual dailyReturn, weeklyReturn etc not working. What do ...
0
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0answers
17 views

Extract the short-run and long-run volatility of any time series with component sGarch (rugarch)

I try to estimate a component sGarch model with the rugarch package in R. My goal is to extract the short-run and long-run volatility components of any time series. I am not interested in the ...
0
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2answers
107 views

Option pricing without analytical solutions

I am quite new to the topic of financial options. I'm aware of options with analytical solutions (e.g. European options in Black-Scholes and Ornstein-Uhlenbeck models). I read that sometimes (most ...
0
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1answer
52 views

Futures vs. spot forecasting

If i have the belief that the futures lead the spot for price discovery, and I am able to forecast the future prices, given this forecast, what would be the best way to back out this number such that ...
1
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0answers
26 views

Optimized search for yield-to-worst of a callable bond

Suppose that I need to find the yield-to-worst of a callable bond, and that the option is American (call any time). The bond may have step-up coupons and/or non-constant call price (oprion strike). ...
0
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0answers
38 views

How to calculate out-of-sample and in-sample Sharpe Ratio?

I am conducting a backtest on different investment strategies and would like to calculate (i) the out-of-sample Sharpe ratio and (ii) the in-sample Sharpe ratio according to "Optimal Versus Naive ...
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0answers
23 views

Cash account growth in Burgard & Kjaer (2011)

I am rereading [1] and there is something I cannot get my head around this time. In Section 3, page 6 of the paper, they derive the growth of the cash account when the hedging portfolio includes the ...
0
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1answer
60 views

Translating Order books accounting for fees

I am trying to understand how fee structure plays into how I should best execute a trade. Say there are two exchanges with the following order book: Exchange A: Bid Qty | Bid Price | Ask Price | ...
0
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0answers
60 views

Pnl Explanation using R (blotter)

I have a portfolio of stocks based on a proprietary strategy. I would like to explain the Pnl over a period, for example I would like to find the pnl contribution of each name of the period. Is there ...
1
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0answers
90 views

Process Transforms (Fractional Difference)

Let's say I have a process $X_t$ with unknown variance process $V_t$. Then, I write $\mathrm{EMA}[X_t]$ to be the 5 sec exponential moving average of $X_t$. Consider the transformation $$\sum (X_t-\...
1
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2answers
63 views

Why do some mutual funds or indexes have an average effective maturity that is way larger (2-4 times larger) than the average effective duration?

I would like to know if this difference occurs when the coupon payments are very large and/or if there are other reasons.
2
votes
1answer
86 views

Covariance - Negative Portfolio

How do you calculate the one day standard deviation (in dollars) for a portfolio that is short $30,000? How do you calculate the weightings to use? I already have the necessary covariance matrix.
1
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1answer
77 views

Benchmark of a Dollar Neutral Strategy

A dollar neutral strategy invests the same amount of money long and short without accounting for the volatility (risk) of either side. Depending on volatility you either end up positively or ...
1
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0answers
66 views

How to price a put option on a multi-asset fund? Confused by risk-neutral pricing implicaton on real world

The fund has super track record with stable vol. The chance for this Put to pay out is very low in real world, but a B/S risk-neutral pricing would give a very high cost. I am struggling with the ...
0
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1answer
85 views

Why meta-labeling is is robust?

With all due respect, I saw this technique in the book , Advances in financial machine learning, but I found that it acts like a filter for the trades only. And it seems doing the job of overfitting ...
0
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0answers
69 views

Quant in rates modeling wanting some insight/advice about buy-side [closed]

So I work in a BB bank as a quant in its rates modeling team which is a part of quant research group. I intend to work in the buyside a fews years down the line, with ambitions like opening my own (...
2
votes
0answers
52 views

Average Strike Option with bounds

I'm looking to price a call option with an exotic feature. The price I'm trying to calculate at time $t=0$ is \begin{equation} C = E^\mathbb{Q}[(S_T-K_T)^+] \end{equation} where $S_t$ is the stock ...
0
votes
1answer
32 views

Do NASDAQ and Russell 2000, 3000 Indices have total return indexes for gross and net? What are they labeled?

Do NASDAQ and Russell 2000, 3000 Indices have total return indexes for gross and net? What are they labeled? I know the S&P has a gross TR index with the ticker SPTR and net SPNTR, so I'm ...
0
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1answer
106 views

How to extract standard deviation from normal distribution in R

If I have some point forecast and an 80% confidence interval, with the forecast assumed to be normally distributed with a constant variance, how do I extract the actual variance? Let us work with the ...
9
votes
1answer
296 views

No arbitrage conditions for normal implied volatility

usually the term implied volatility refers to Black-Scholes implied volatility (also Log-Normal volatility): it is defined as a quantity which when plugged in the Black-Scholes formula returns the ...
1
vote
1answer
76 views

Linking PD and LGD

I am trying to solve the equation for PD but struggling to bring it to the LHS. Any ideas as to how I can do that? $$ LGD = \frac{\Phi \left [ \Phi^{-1}(DR) - \frac{\Phi^{-1}(PD)-\Phi^{-1}(PD\cdot ...
0
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1answer
64 views

How to calculate Money-weighted Rate of Return when there are multiple negative cash flows during investment period?

I know that when there are multiple changes of sign in the sequence of cash flows of a project, the project may have multiple IRR, which render this criterion impractical. Therefore, in such ...
14
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1answer
614 views

Can we use White's reality check to compare two Sharpe ratios?

I read a paper from Ledoit and Wolf that proposes a method to compare two Sharpe ratios and a paper from White that proposes a method to compare $n$ trading rules. My question is: Can we use White's ...
0
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1answer
82 views

Why are Interest Rate Swaps not valued using Monte Carlo Simulations?

the current valuation methods seem to rely on treating the floating payment as deterministic based on the current yield curve and derived forward rates. But wouldnt it make more sense to use monte ...
0
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1answer
79 views

Calculating YTM for a floating rate bond

I am trying to understand how YTM's are calculated for floating rate notes. I have had a go at calculating it and I am always a few bps off for every FRN I try to calculate. Does anyone have any ideas ...

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