4
votes
2answers
95 views

Probability that realized volatility is larger than implied volatility

I did a test about quantitative finance. One of the question was : What is the probability, in the Black-Scholes world, that the realized volatility is larger the implied volatility ? And why ? ...
1
vote
2answers
32 views

EUR issuance using forwards to hedge FX risk

Trying to think about the right way to hedge a EUR denominated issuance from FX risk only. Say I have an annual pay 20-year EUR bond and I want to hedge the FX risk but take the interest rate risk. I ...
4
votes
1answer
74 views

Swaption Volatility Cube arbitrage

How can I exploit an arbitrage by violating the following no-arbitrage condition (taken from the paper "Arbitrage-Free Construction of the Swaption Cube" by Simon Johnson and Bereshad Nonas): ...
1
vote
0answers
34 views

Price compounding: Swap versus Governments Bonds

There are different rates curve to compound prices. Since the crisis, regulators tends to favor price compounding with swap curves over IR curves deduced from governments bonds (EU regulators, french ...
4
votes
2answers
98 views

How was the old VIX calculated?

Today VIX is computed based on near- and next- term options series which fall into the time period of [23, 37] days. That is what it is now, when they use SPX weekly, so they have options expiring ...
1
vote
0answers
12 views

Why use Moody's KMV EDF for one year

If I were to use Moody's KMV proprietary database with expected default frequqncies(EDF) for sectors and countries, along with aggregations for financials and non-financials, significant banks etc: ...
4
votes
1answer
69 views

Covariance of Log-Normal Variables

In Obstfeld and Rogoff (2000), formula (12) states the following: $$ W = (\frac{\phi}{\phi-1}) \frac{E\{K(L^\nu)\}}{E\{\frac{L}{P}C^{-\rho}\}} $$ where $\phi$, $\rho$ and $\nu$ are parameters, $E$ ...
1
vote
1answer
73 views

Discount factor

Suppose we have : $r$ - zero coupon rate, constant over time, $n$ - a number of years (an integer), $\theta$ - a fraction of a year $(\theta < 1)$ , calculated with the relevant day count ...
5
votes
0answers
53 views

simulating from the CIR++

I am looking at the CIR++ model which is described in interest rate models by Brigo et al, and was wondering on how to actually simulate from this model. The model reads $$r_t=x_t+\phi(t),$$ where ...
2
votes
2answers
56 views

Best practice for international Fama-French analysis

First I have to admit that I have never been really good at thinking about the implications of investments in different currencies. I don't know why but it makes my head spin, this is why I am no FX ...
1
vote
1answer
35 views

Rate of Options decay

I know "Time decay accelerates on nearing expiry". But I want to know the rate of acceleration. How curvy is the theta curve? Answers could be like, Provided IV is stable, in a 3-month ...
1
vote
1answer
24 views

How to value pricing and ratings? How to quantify best value? [closed]

I'm trying to define which hotel offers the best value. Let's say we have two hotels - A and B. For A, you pay $10 a night and the rating for the hotel is 9.8. For B, you pay $8 a night and the ...
4
votes
1answer
76 views

What is the best / most used / recommended C++ non-blocking networking library for low-latency / real-time development?

I'm coming from Java and there we use the EPoll selector implementation that comes with the JDK for non-blocking / asynchronous networking TCP and UDP development. Therefore you don't have to make ...
1
vote
0answers
16 views

Multi-factor APT model in practice: non-zero mean factors, observations needed and portfolios

I'm going to build a multi-factor APT model for the Swiss market starting from the work made by Chen, Roll and Ross (to which I will add and test some additional factors). I have some doubts though: ...
2
votes
3answers
65 views

Sensitivity of short-term vs long term options' IV

I could see that the short-term options' IV raises on earnings announcements when longer-term options' IV does not react too much. So I had this doubt, "Is the volatility of short-term options' IV ...
6
votes
0answers
126 views

Transforming 3M volatilities into 6M volatilities in EUR forecast curves

I have implemented a bootstrapping algorithm to extract forward volatilities from cap/floor flat volatilities for different currencies. I am however struggling a bit when implementing a method to ...
1
vote
1answer
82 views

Monte Carlo Option Pricing: Averaging Price Per Path

In Glasserman's book, he computes the price of an option by first computing the average price over each simulated price path. Once all the paths have been simulated, the average of all the payoffs is ...
1
vote
2answers
109 views

What does a negative stock amount mean in a single-period, binomial market model?

Consider a single-period, binomial market model with a $r > 0$ interest rate (in USD per period) and a portfolio $(x, y)$ consisting of two assets: a savings/lendings account and a stock, both ...
0
votes
0answers
31 views

IV of stocks vs IV of options

As for as I have seen, Implied volatility of stocks are easy to understand as there will always be a peak and fall(usually on earnings announcement dates). The magnitude differs but the wave pattern ...
5
votes
1answer
87 views

Square of arithmetic brownian motion process

We have an arithmetic Brownian motion process $X_t$ that follows $dX_t=\mu dt + \sigma dZ_t$ and we define the asset price $S_t=X_t^2$ and we are asked to find the stochastic differential equation ...
1
vote
3answers
36 views

Swap curve and short maturities

Consider USD Libor 3M swap curve. There are different maturities: 2d, 1m, 3m, 6m, 9m, 1y, 18m etc. The values for 3m, 6m, 9m etc. time buckets are just swap rates for swaps with floating leg equal ...
0
votes
0answers
13 views

Proving the convexity of put price [duplicate]

Prove that the price of the European put option is a convex function of the strike price in one-step binomial model. In other words, if $P_E(X)$ is the price of the European put option in one-step ...
0
votes
0answers
39 views

Portfolio replication option pricing: Money market position

Why when replicating a call option, the money market position (bond, risk free investment) is negative and when replicating a call option, the money market position is positive? Please explain ...
4
votes
2answers
99 views

Cost of rolling futures contracts

Futures are traded on margin, so that the P&L of any open position is realized on the posted margin. To maintain a constant exposure to the future, an expiring contract needs to be rolled into a ...
0
votes
1answer
43 views

Bilateral Counterparty risk

Why do counterparty risk pricing adjustments need be considered in a bilateral counterparty risk perspective? Thanks
1
vote
2answers
52 views

what data sources are useful for obtaining financial statement data of listed companies NYSE and NASDAQ?

Exactly, I need balance sheet, income statement, cash flow statement, stock market, bankruptcy situation, fraud situation and corporate governance data of companies in USA. Thanks beforehand,
1
vote
1answer
51 views

Put-on-call option confusion

So the question asks: Given a 3-steps Binomial Tree model with $S(0) = 50$, $U = 20%,D = 􀀀20%$, and $R = 5%$. A European call option has the strike price $X = 40$ and maturity time $T = 3$. Also, a ...
4
votes
2answers
86 views

What is the arbitrage opportunity in this simple one-period market?

I have a single period market, and three states, and I have 3 risky assets. I assume no interest. So I have three states $\Omega=\{\omega_1,\omega_2,\omega_3\}$. All assets start with the value 1, ...
1
vote
1answer
62 views

How to calculate the NPV (Net present Value) in this question? [closed]

A company pays £1,200,000 to purchase a property. The company pays £30,000 at the end of each of the next six months to renovate the property. At the end of the eighth month the company sells the ...
1
vote
1answer
42 views

Put call parity: when are the premiums the same?

Please explain why put call parity could be compared to the payoff of a long forward contract. ie. $C_E-P_E=V_X(0)$ where $C_E,P_E$ are the call/put premiums and $V_X(0)$ is the value of a long ...
0
votes
1answer
37 views

Replication strategy of European call option

So the question asks: L et $S(0) = 120$ dollars, $u = 0.2$, $d = −0.1$ and $r = 0.1$. Consider a call option with strike price $X = 120$ dollars and exercise time $T = 2$. Find the option price and ...
1
vote
1answer
73 views

What qualifications do the traders have that quants don't?

What qualifications do the traders have that quants don't? I know that they are not expected to know as much math, but that can't be it, can it? (I'm not in finance, nor am I really planning to go ...
5
votes
3answers
83 views

Can call options be priced with Least-Squares Monte Carlo?

I have been reading about Least-Squares Monte Carlo (using Longstaff & Schwartz algorithm) for option pricing. So far, I have only read examples that uses LSMC for american/bermudan PUT options ...
0
votes
0answers
14 views

Calculating portfolio returns from a dynamic, optimal re-balancing strategy

I am calculating a dynamic strategy with optimal re-balancing as in here. As a result of maximizing the expected utility function I obtain the weight for the risky asset in period $t=0$. All such ...
1
vote
0answers
6 views

What are appropriate algorithms for forecasting contract schedules to maximize profit?

Imagine a situation where a business negotiates contracts for the maintenance of widgets it sells. Situation Customer buys 20 widgets. Customer negotiates contract for widgets to be ...
0
votes
1answer
65 views

Calculating half life of mean reverting series with python

I am currently attempting to calculate the halflife of a mean reverting series using python programming language and the theory of the Ornstein–Uhlenbeck process. I have a series which when plotted ...
1
vote
1answer
23 views

Indexes and return spreads

First and foremost thank you for reading my question, I hope all if you have a Happy Holiday this weekend. On to my question: I am completing an assignment on global sovereign bonds, I've been ...
1
vote
2answers
31 views

Maximization with risk-neutral investors and VaR constraints

In this paper, the authors make a simple model with: (1) A global bank, who is risk-neutral but has a Value-at-Risk constraint: $$\max_{x_t^B} E_t[x_t^B\prime R_{t+1}]$$ s.t. $$\alpha ...
0
votes
0answers
31 views

Connecting Call price computed discretely to call price computed under continuous time case

I want to connect the call premiums calculated discretely via the binomial pricing method to the Black-Scholes-Merton formula for the call premium which applies to continuous time case. The framework ...
0
votes
3answers
100 views

What assets other than bonds are risk free?

I saw a question the other day that said Assume you have only two assets to build a portfolio. Name and explain three scenarios under which a completely risk-free portfolio can be formed? I ...
0
votes
0answers
12 views

One period optimizations with tcosts, few predictions and getting positions unstuck

Consider a one period portfolio optimization with objective that maximizes $\omega E(r) - \lambda_r\omega^t\Sigma\omega - TC$ Where TC is however we calculate tcosts/impact. Importantly, most ...
0
votes
0answers
19 views

Determining Monthly Premium with Credit default swap

I hold a 10 year, $100 million bond. In order to minimize risk, I enter into a credit default swap in which I am paid every time (monthly) the bond rating drops to a new low. I have the probabilities ...
9
votes
2answers
264 views

Solution of Merton's Jump-Diffusion SDE

In many textbooks and also in the original Merton's paper the solution of the SDE $$ dS_t = S_t\,\mu\,dt+S_t\,\sigma\,dW_t+S_{t^-}\,d\left(\sum_{j=1}^{N_t}V_j-1\right) $$ is written as $$ S_t = ...
1
vote
0answers
21 views

How to calculate the unrealised profit on sinkable bond

How is calculate the unrealised profit on Sinkable Bond when 50% of the bond value already been paid? Is the following method correct: Unrealised P&L = ((Current.Position * Market.Price) - ...
3
votes
1answer
65 views

The Relation Between the Ricci flow and the Black-Scholes-Merton Equation

Grisha Perelman once wrote that The Ricci-flow equation, a type of heat equation, is a distant relative of the Black-Scholes equation that bond traders around the world use to price stock and ...
0
votes
0answers
36 views

First step of Black-Litterman portfolio

I tried to implement Black-Litterman model. I have a covariance matrix, market capitalization for each asset. I assume a risk aversion factor to be 10. First I use the following code to get ...
4
votes
2answers
67 views

Realized “efficient” frontier. Is this reasonable?

I have performed some out-of-sample analysis of mean-variance optimization with monthly rebalancing. Studying the "realized efficient frontier", I am worried that something is wrong. Since the ...
3
votes
2answers
95 views

A proof that the final payoff on a futures contract is twice that on a forward contract

Following is an argument demonstrating that the final payoff on a futures contract is twice that on a forward contract, contrary to what I believe is the accepted truth that the two payoffs are the ...
0
votes
1answer
40 views

Zero-rate USD Curve

Good day, I have inputs: Libor 1D, 1M, 2m, 3m. FRA 3x6, 3x9, 3x12 IRS 2Y, 30Y. What formula should I use to construct zero rate curve? Thanks
1
vote
1answer
36 views

What exactly do I sell when I sell a futures contract I have previously bought?

Suppose I buy a futures contract and later, before expiry date, I sell it out. Is something physically exchanged between myself and the buyer, e.g. a paper certificate specifying the contract's ...

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