# All Questions

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6 views

### How to calculate mean annualised returns

I am trying to calculate the mean annualised return for a fund using historical monthly returns but I am having difficulty in finding an appropriate method to do so.
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### Python Quantlib : How to value the Non Deliverable Interest Rate Swaps?

I followed all the procedure in Quantlib to process interest rate swap valuation through Python Quantlib. I valued more than a million records. All the valuation is almost the expected amount. But '...
25 views

### Where does the “Rule of 72” comes from?

I was watching this Khan Academy video. The question is: if I deposit $C$ in a bank that pays an interest rate of $r%$ compounded annually, how long does it take to double my money? Doing the math ...
19 views

### What is the difference between “Notional” and “Nominal” values?

Actually I am facing a huge discussion at work about the vocabulary we are using to test products. We keep returning on the question; when do we use the term "Notional" and when do we use "Nominal" I ...
35 views

### Outperform the market with a Beta lower than 1, is it possible?

I have a portfolio which seems to have outperformed the benchmark for the past 2 years however the risk system I use advises that using recent past data (lookback period of 2 years) the Beta to this ...
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### Throwing a dice and risk neutral probability

Consider the game of throwing a "fair" dice. Not sure if the answer is obvious but is there any proof (e.g. replication argument) that under the risk neutral measure the probability of any outcome is ...
60 views

### Solving Stochastic Differential Equation

Given the stochastic differential equation: $$dZ_t = -Z_t \theta_t dB_t, \quad Z_0 = 1.$$ for an adapted process $\theta_t$ and Brownian motion $B_t$, how exactly do I apply Itô's Lemma to obtain: ...
62 views

### Recruiter from large firm asking for where I was submitted [closed]

I am copying the question posted on workplace SE below: https://workplace.stackexchange.com/questions/153937/recruiter-from-large-firm-asking-for-where-i-was-submitted I decided to ask here as well, ...
36 views

### How many seconds of Longstaff Schwartz would it take to get machine accuracy?

Roughly speaking, using a standard programming language, a standard computer, and a standard implementation, how many seconds would it take to price an American put option to 10+ digits of accuracy in ...
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### L2 Assumptions of the Longstaff Schwartz method

In page 121 of the original LS Paper they use the fact that the space of functions they are dealing with (payoffs of American options), belong to the $\mathcal L^2$ space. They use this assumption ...
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### American option pricing [closed]

Let $C(S,T)$ an american call option with maturity $T$ on the underlying $S$, then: 1) The price of the derivative is greater than the equivalent European call option 2) The higher the delta, the ...
31 views

### Delta approximation of an option [closed]

If f(t,s,sigma) is the price of an option, where t is time, s is the spot price of the underlying asset and sigma is its volatility,ù which of the following quantities is an approximation of option ...
55 views

### Vanilla option pricing at different points in time

Let $C(t) = C(t; S,K,T)$ the price at time $t$ of a plain vanilla call option with maturity $T$ and strike $K$ on an underlying $S$; if for $t_1<t_2$ we have $C(t_1) > C(t_2)$, it could not be ...
43 views

### What does “invest in portfolio volatility” mean?

In this paper, Barnea, Amir, Henrik Cronqvist, and Stephan Siegel. "Nature or nurture: What determines investor behavior?." Journal of Financial Economics 98.3 (2010): 583-604. it is mentioned ...
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### Expected growth of a function of a GBM [closed]

Suppose that $S_t$ follows a Geometric Brownian Motion and that $Y_t = F(t,S_t)$. Let $\sigma_S$ and $\sigma_Y$ be the volatilities of $S_t$ and $Y_t$ respectively. If the expected return of $S_t$ ...
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### Prerequisites to learn Quantitative Trading [closed]

I am a computer science student and I wanted to get into quantitative trading. Which parts of trading, finance and economics do I have to learn. Please suggest a path and books or other resources ...
63 views

### Where can I retreive the end of day fx prices?

I'm developing a reporting tool and I need a data source for end of day price data. For example, it should give me the XAUUSD price at a specific date, say 2019-12-05. Do you know such a data source? ...
31 views

### GARCH(1,1) estimation in R via fmincon

I try to replicate Duan's (1995) results on option pricing in GARCH model. I have the same dataset and I follow MLE method described in book Pricing Option under Stochastic Volatility (Pretoria 2003). ...
14 views

### What does it mean when cumulative return intersects or is below the risk free rate?

I am learning about the basics of Risk Adjust Performance when I stumble upon something odd with some sample data about UPS. Clearly, the UPS stock's cumulative return is underperforming the market; ...
24 views

### What can be used as a good proxy for OIS?

I was trying to find a good proxy for OIS. Let's say you have access to USD OIS rates only starting from 2016. What instruments or curves can be used to model OIS such that it can replicate OIS ...
42 views

### Finding the Efficient Frontier in Tensorflow

I have two assets A and B. Asset A has an expected return of 0.92% with a standard deviation of 2.10. Asset B has an expected return of 1.39% and a standard deviation of 2.20. I want to find the set ...
17 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?
43 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 $DF_f$: ...
35 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?
54 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?
38 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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### 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 $0 \le t \le T_p$, ...
60 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-...
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### 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 ...
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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? ...
84 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} \...
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### 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 ...