0
votes
2answers
110 views

Discrepancy between binomial model, Black-Scholes and Monte-Carlo Simulation

I try to use Monte-Carlo Simulation to price a 10-year call option. Based on below parameter, S = 1, X = 1, volatility = 80%, T = 10, risk-free rate = 0.22% The option value based on Monte-Carlo ...
1
vote
1answer
54 views

Portfolio optimization

first I just hope that this question is in the right place. I have started working on portfolio optimization and the formulation of the problem and their solution : For example in the Markowitz ...
0
votes
0answers
11 views

Modified average swap

I have an instrument that is a swap over the SMK6 that at expiry (it has only one cashflow) pays the difference between the average daily Price of the underlying and the actual Price. The average ...
0
votes
0answers
57 views

Risk-neutral probabilities

I will use this theorem 3.2 from the book "Quantitative modeling of Derivative Securities" by Marco Avellandea: Theorem 3.2 - Assume that there is no arbitrage, i.e. there exists a risk neutral ...
3
votes
1answer
108 views

Example of options that cannot be priced with least-square Monte Carlo

Can you give some example of options that cannot be priced with least-square Monte Carlo? Intuitively, this is any option for which a payoff depends on a previous exercise decision. It's relatively ...
0
votes
0answers
20 views

How to appropriately measure volatility in assets with different execution dates?

Let's say I have two assets and I am hedging them with going short on two other assets. Let's say that asset 1 is expected to expire in one day and asset two is expected to expire in two days. Let's ...
0
votes
1answer
47 views

For a call option, what is the real-world probability of expiring in-the-money?

In the Black-Scholes world, the risk-neutral probability of expiring in-the-money is given by N(d2). Can I just replace the risk-free rate by the drift rate to obtain real world probabilities? Thank ...
0
votes
0answers
18 views

Building PD model using Moody's Historical default rates

I want to build a Probability of default model using moody's cumulative default rates. I was trying to calculate the average default intensity rate and from there I dont know where to go. Example : ...
0
votes
1answer
51 views

Matlab code for equally weighted portfolio

I have daily returns of 10 stocks. I need to construct an equally weighted portfolio that goes long in the 3 highest returns and short in the 3 lowest returns. The portfolio needs to be re-balanced ...
4
votes
1answer
60 views

Determining the implied volatility for options with bid/ask prices below the intrinsic value

I need some help in understanding the Black-Scholes option pricing model. In my data there are several deep itm European index put options that have an ask price below the intrinsic value. ...
5
votes
1answer
107 views

Is trading mean reversion of small principal components of prices profitable?

Many have told me that it is a good idea to look at the third principal component (PC) of yield curve movements, as well as third and fourth PC of G10 currencies. They claim these PCs represent ...
0
votes
0answers
17 views

VEC GARCH (1,1) for 4 time series

I have to estimate a VEC GARCH(1,1) model in R. I already tried rmgarch, fGarch, ccgarch, mgarch, tsDyn. Has somebody estimated a model like that? ...
3
votes
0answers
74 views

Ridiculous Bond Prices under Vasicek Model

Has anyone played with the parameters of the Vasicek model and observed the sometimes ridiculous bond prices it implies? E.g. with the right parameters, a 30-year zero is priced at $147,327. To be ...
0
votes
1answer
75 views

Open interest and short selling

Open interest of SPY: https://finance.yahoo.com/q/op?s=SPY+Options If someone sell short a contract the open interest adds up or down? The open interest on yahoo finance is a reliable Information of ...
0
votes
0answers
9 views

How to get currency denomination of security from yahoo finance API

I'm trying to write a portfolio program and it would be nice if it could auto detect what the currency denomination of the ticker is without needing user input.
0
votes
1answer
68 views

Who Uses American Options?

...in other words, why would a person want to have the right to exercise an option early? What advantage does that really give you? Are Euro-style options not good enough for some people? Who are ...
0
votes
0answers
31 views

Hedging portfolio of options with different underlyings

Suppose i have call options for 90 of the 100 stocks of NASDAQ100. How can i hedge the risk using NASDAQ futures? Also, how can I get rid of the residual risk?
3
votes
0answers
39 views

How does a Broker-Dealer lend shares to other Broker-Dealers?

Is it possible to find out how a OTC Broker-Dealer in thinly-traded equities lends shares for short-sales to other Broker-Dealers. Which platform or process is involved?
3
votes
1answer
101 views

Spectral and distortion risk measures

Is there any difference between the spectral and distortion risk measure? Or is it just a different name for the same kind of risk measure?
1
vote
1answer
44 views

How to measure if investors are diversified in a stock market?

My question is related to this question but it is not the same. Consider the US stock market. How can I tell if people trading in this market hold properly diversified portfolios? Is there some ...
5
votes
1answer
86 views

Modelling EUR/USD with Ornstein-Uhlenbeck + jumps?

I'm trying to simulate a process as close as possible to EUR/USD of the ten past years. I've used a Ornstein-Uhlenbeck process: $$d X_t = -\theta (X_t - \mu) d t + \sigma d B_t$$ with the ...
5
votes
2answers
79 views

Is it possible to deal with non-normal distribution in Black-Litterman model?

Suppose that I know that the normality assumption about my data is unrealistic (as it is very frequently): is it possible to apply any distribution that I judge the right one to the Black-Litterman ...
1
vote
0answers
29 views

Determining rate of interest

If I have trade prices of 10Y futures contract (ZNH6) is it possible to derive the interest rate from it? Or is there a better way to obtain historical 10 year rates?
1
vote
1answer
39 views

Deriving a 3M libor curve from 6M libor swaps and 3M-6M libor basis swaps

If I had a set of 6M Libor instruments and another set of 3M-6M basis swap instruments, how would I derive the 3M Libor curve? Just bootstrap the 6M curve and the basis curve and add up the zero ...
1
vote
1answer
29 views

Are Variances generally stable for any given instrument?

My hesitation, as I look at getting into forecasting based on observed variances, is the nagging question - if variances are not constant per-instrument, is it any good to use the last month or year's ...
-1
votes
1answer
69 views

Black_scholes formula for a butterfly option

Im wondering if I can apply Black-Scholes formula to valorate a butterfly option, i.e: $$B(T)=Vcall(S(T)-K,0)+Vcall(S(T)-K',0)-2Vcall(S(T)-K'',0)$$ with $K<K''<K'$, just evaluating each call ...
0
votes
1answer
42 views

Monetary Policy and the Yield Curve PART TWO

The Fed has a number of tools/targets with which they manage monetary policy. I'm looking to refine a concise summary of them and looking for guidance/correction/validation. Think I understand these ...
0
votes
1answer
30 views

Equitable Allocation

This questions borders on the actuarial side of things but the general solution should have relevance in several situations. Suppose we have a set of $k$ people who will retire in $\{n_1,...,n_k\}$ ...
0
votes
0answers
38 views

How to backtest Value at Risk Models using Conditional and Unconditional tests?

I am trying to carry out backtesting on a number of Value at Risk figures i obtained using var/covar, historical, and monte carlo simulation. The two methods im using are the Kupiec test ...
1
vote
1answer
34 views

About the Feller Condition in Heston Calibration

I have noticed when reading (many) articles about Heston Calibration that not all (few actually) do care about the Feller condition. Below is a compilation of calibration results from some different ...
0
votes
1answer
32 views

Variance covariance matrix for a portfolio containing bonds also with other asset classes

What should we take for a bond or a zero coupon bond in order to make a variance covariance matrix? For example:- Equities - we take the market price Cash - we take the spot rates Bonds - Do we take ...
2
votes
1answer
43 views

Integrated volatility

Can someone give me an explanation of what integrated volatility is (and possibly why it is preferred) versus a standard measure of volatility eg variance?
1
vote
0answers
53 views

School project about Black Scholes with stochastic volatility

In a university project I am looking at Black Scholes model with a stochastic volatility. I’m still not quite sure about my focus (I am in the beginning 'Idea phase'). I want to explain the theory ...
2
votes
2answers
93 views

Free high resolution financial data

As thebonnotgang(1) stopped updating their database, I was wondering if there are some other free sources of high-frequency data available. I found a proper tick data api (ca. 25 day history) hosted ...
0
votes
0answers
53 views

Arrow-Debreu model

Consider an Arrow-Debreu market with $M = 2$ which consists of a bank account with interest rate $R = .01$ and a forward rate of a non-storable asset with maturity of one period. The futures price is ...
0
votes
1answer
70 views

Ratio of gaussian CDFs in Black-scholes option pricing formula

What is meant by $\frac {\Phi (d_2)}{\Phi (d_1)}$ in the Black Scholes call option price? I found it in a solution as $\frac{\text{short position in cash}}{(\text{number of shares})(\text{strike ...
0
votes
0answers
24 views

Eurostoxx50 data in USD

does anyone know how I can import from yahoo the Eurostoxx50 data denominated in USD (not Euros as listed on yahoo?)
0
votes
0answers
12 views

building a correlation of equity portfolio to custom benchmark 60/40

Hi i have built a custom portfolio of equities with weights but would like to plot the daily, monthly and annual correlation to 60/40 benchmark. Please see code below and suggest how I can do the ...
0
votes
1answer
50 views

Step By Step method to calculating VaR using MonteCarlo Simulations

In trying to find VaR for 5 financial assets with prices over a long period of time(2000 days worth of data) how would I do the following: Carry out monte-carlo simulation in order to find a VaR ...
1
vote
0answers
50 views

Monetary Policy and the Yield Curve PART ONE

As I understand it, the Fed has 3 tools for moving interest rates to combat inflation/unemployment: the discount rate, Fed Funds rate and open market operations. I'm trying to understand how the ...
0
votes
1answer
24 views

What does continuously payable annuity mean?

I am preparing for F< exam but I am unable to understand the meaning of continuously payable annuity. What does it mean? An example would be great.
1
vote
1answer
41 views

Delta of a Commodity Future

Generally the price of a future is $ F(t,T) = S(t)e^{r(T-t)}, $ and it's delta is: $ \frac{\partial F}{\partial S} = e^{r(T-t)}. $ (As opposed to the delta of a forward which is always one.) In ...
0
votes
0answers
15 views

Academic definition of portfolio turnover

I'm looking for an academic reference on how compute the standard portfolio turnover used in finance. I found a definition by Barroso and Santa-Clara, however their definition is based on both the ...
2
votes
0answers
90 views

Equity Index Announcement Data

Does anyone know of a data source that provides announcements of future index events (adds/drops/re-balances), specifically for equity indexes? I know these are mostly available somewhere on each ...
0
votes
0answers
32 views

Most recent work on American option **ANALYTIC** pricing

I am studying American options and inquisitive on why they lack an analytic pricing formula. I found a paper by Kim,1990 on analytic valuation of these options and then Byun,2005 paper which studies ...
-1
votes
1answer
23 views

Why is it cheaper to repay monthly loan at the start of the month [closed]

Assuming I borrow $50000 from the bank where the details are as follow ...
3
votes
1answer
62 views

What is the heat-map method of calculating VaR?

I'm familiar with the historical full revaluation, VcV, and Delta-gamma methods, but a client keeps talking about a heat-map method and I'm not sure what he's talking about. Any ideas?
1
vote
0answers
51 views

How was this probability of negative U.S rates by end 2017 calculated?

http://www.bloomberg.com/news/articles/2016-01-26/bets-on-negative-u-s-rates-by-end-2017-jump-above-10-chance Options markets show some investors are taking out protection in case rates instead ...
1
vote
1answer
43 views

How to get the the final % return in backtesting?

I'm learning how to do backtesting in Python using Pandas. I'm learning how to use Moving Average Crossover. I've generated signals to buy or to sell already. But I'm not sure where to go from there? ...
3
votes
2answers
64 views

Bounded Stochastic discrete process

I just came across this stochastic process (link): $dY_t = (a-bY_t)dt + c \sqrt{Y_t(1-Y_t)}dW_t$, where $dW_t$ is a Wiener Process. According to the author under certain conditions this process is ...

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