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1answer
65 views

Why does a higher stock value imply a higher call option value [closed]

This may seem like a very dumb question, but if the underlying stock price is greater, then why should a call option be worth more. My reasoning is that, if the option price is not affected by the ...
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votes
2answers
144 views

Calculating units in a cross currency short trade

If I have a forex account with a broker and a balance of 100 USD, and I'd like to short EUR/JPY, how many units can I short? How is this calculated? Which currency pair do I use to translate between ...
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votes
1answer
5k views

Stub rate and first fixing in IRS

I have 2 questions that probably are related. Suppose there is an IRS that pays a 2% fixed rate every 6 months and receives the Libor 3 months (but paid every 6 months). The swap starts today (March ...
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votes
1answer
142 views

Possible to use diffusion equation(s) to price derivatives with non-zero boundary conditions?

One of the reason the Black-Scholes can be transformed into the heat equation is that calls and puts have a zero boundary condition on their contingent payoffs. Define the terminal payoff condition ...
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votes
1answer
155 views

FX Option Pricing Under Basis Adjustment

Given money market rates such as USD LIBOR and EURIBOR and in the context of FX options valuation, I have been reading about the importance to include a so called basis adjustment to one of the ...
0
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1answer
770 views

QL-Python Bootstrapping Yield Curve FuturesRateHelper throwing off results

I'm trying to perform a bootstrap of a yield curve from deposit rates, futures, and swaps, and the interpolation is "blowing up" for the futures maturities being off by two orders of magnitude (100x). ...
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2answers
1k views

What’s the derivative of the sharpe ratio for one asset? Trying to optimize on it for a model

It seems most Sharpe ratio derivations seem to be for portfolios but I am just tracking a single asset? $SR = (r_p - r_f) / \sigma_p$ but what would I derive with respect to for an optimization/ ...
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0answers
142 views

Monte Carlo simulation error estimation

How does one estimate the error of a Monte Carlo simulation, for example, of the price of a European call under the Heston model with a given step size and number of paths?
0
votes
1answer
126 views

What does “1-month horizon” mean in VaR calculations

For a simple equity portfolio, I need to compute historical 1-year simulation VaR with a "1-month horizon". I imagine this means I need to compute the 1-month return of the portfolio at each point in ...
0
votes
1answer
70 views

How to calculate Chande Momentum Oscillator for FX

I am trying to calculate a momentum oscillator for the EUR/USD pair and am confused. A formula I read referenced the sum of previous up days. What is a "day" considered in Forex?
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votes
2answers
446 views

How is the price of a bond actually determined?

How the price of a bond is actually determined? Is it the supply-demand that determines the price first and then the YTM is calculated on the back of this for that bond. Or is it that the changes to ...
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votes
1answer
981 views

PCA on term structure of interest rates

Interest rate time series seems to be non-stationary whenever test is performed But covariance or correlation matrix is derived from term structure time series which are non stationary and later PCA ...
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1answer
106 views

Calculating historical Bond returns

How would you calculate historical bond returns using bond prices? Would you treat bonds just like shares ? Thanks
0
votes
1answer
932 views

Getting the next price of a GBM (Geometric Brownian Motion)

I am writing a program that creates realizations of a GBM. Starting from an initial price, I get the following price with this formula: ...
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2answers
1k views

FX Option pricing on Forward vs. Spot

In a GBM world with riskless domestic and foreign interest rates, what would be the correct model for a FX plain vanilla option given the statement that this option is priced on the forward? I guess ...
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votes
2answers
222 views

Valuation of FX vs. Commodities Barrier Options

With reference to my previous question about the computation of a barrier option delta, @LocalVolatility referenced a nice closed form solution to value barrier options on a stock paying a dividend ...
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1answer
2k views

Price of call/put is convex in $K$ (strike price)

Let $\lambda\in(0,1)$. Then $$C(T, \lambda K_1 + (1 - \lambda)K_2, S, t) \leq \lambda C(T, K_1, S, t) + (1 - \lambda)C(T, K_2, S, t)$$ $T$ - the maturity $K_1$,$K_2$ - Strike prices $S$ - stock ...
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votes
1answer
237 views

Finding historical data for indices [duplicate]

Where can I find historical data for option prices on a given index ? Ideally I'd like to find for a period of several months 1) historical prices on options on a given index 2) historical prices on ...
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votes
3answers
960 views

Parametric/Analytical VaR

Suppose I want to calculate VaR for a known distribution with mean $\mu$, variance $\sigma^2$ and $\alpha$-quantile as, $VaR_{\alpha}$ = $\mu + \sigma q_{\alpha}$. For a Gaussian distribution it is ...
0
votes
1answer
2k views

Given $S$ is a Geometric Brownian Motion, how to show that $S^n$ is also a Geometric Brownian Motion?

Suppose that a stock price $S$ follows Geometric Brownian Motion with expected return $\mu$ and volatility $\sigma:$ $$dS = \mu S dt +\sigma S dz$$ How to find out the process followed by variable $...
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2answers
552 views

Mark Joshi, Quant Interview Question problem 2.34; replicating a digital option on a 4-step symmetric binomial tree

Question: Team $A$ and team $B$, in a series of $7$ games, whoever wins $4$ games first wins. You want to bet $100$ that your team wins the series, in which case you receive $200$, or $0$ if they ...
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votes
1answer
346 views

Momentum strategy cumulation of K-monthly returns over multiple months [duplicate]

In a momentum strategy, every month you form a portfolio of winners. Each of these portfolio you hold for K months. So after K months you sell the 1st portfolio, after K+1 months you sell the next and ...
-1
votes
1answer
389 views

If I am very fast (less than 10 microseconds latency) what would be the first strategy to execute? [closed]

Let's assume I found the holy grail of low-latency trading (which I didn't). For educational purposes, what would be the first strategy I would direct my trading code?
-1
votes
1answer
129 views

What is the connection between the federal funds rate and US government bonds

If the Federal Funds Rate changes, does that affect bond prices? How? Also, is there any connection between the Federal Funds Rate and the coupon payment on US bonds?(for those that have a coupon ...
-1
votes
1answer
1k views

Calculating arbitrage- S&P 500 stocks vs S&P 500 Index future?

How exactly would I go about investigating whether the S&P 500 stocks were currently over-valued compared with the price of the S&P 500 Index futures contract? Is it just a case of taking each ...
-1
votes
1answer
156 views

Use random-shift Halton sequence to obtain 40 independent estimates for the price of a European call

Background Information: Random-shift Halton sequence: Consider the first six Halton vectors in dimension $2$, using base $2$ and $3$: $$\begin{bmatrix} 1/2\\ 1/3 \end{bmatrix}, \begin{bmatrix} 1/4\\ ...
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votes
1answer
299 views

Accuracy for GARCH models

How does one calculate the accuracy of forecasts given by GARCH models considering GARCH is run on returns. Assuming GARCH is a derivative of a regression based prediction model, would regular ...
-1
votes
1answer
111 views

Separate market and limit orders from market depth/tick data

From the website https://www.algoseek.com/equities/, we can get a sample of the full depth market/tick data. From the paper https://arxiv.org/pdf/1710.03870.pdf page 8, I would like to extract the ...
-1
votes
2answers
377 views

Close form solution for Geometric Brownian Motion

I have a very fundamental problem, please help me out. I am little confused with the derivation for the close form solution for the Geometric Brownian Motion, from the very fundamental stock model: $$\...
-2
votes
1answer
453 views

How would you price an option with payout ln(St) where St is the stock price at time t

I know it has to be done through martingales, but I am not fully sure how to do this BSM pricing.

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