# All Questions

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### Discrete Hedging of Options

Assume that a stock $S_t$ follows simple geometric Brownian motion. Let's say we sold option whose payoff is $f(S_T)$. Now, we are only allowed to trade 2 times in the interval [0,T]. What kind of ...
315 views

### Examples for the option model validation

When implementing a code for the new model, even if it provides sensible price, it is still a good idea to compare it against some benchmarks, even in the special case of constant volatility Black-...
22 views

### Overstating Interest Rates?

I'm fact checking my analysis, so there's only one possible answer in that I'm either right or way out in left field (wrong). A friend of mine mentioned this bitcoin lending site and I looked at it ...
40 views

### Is there a considered floor for variation the 1st principal component must explain?

I am wondering if there is a considered floor to the percentage variation the 1st principal component must explain in general for PCA - ie. any lower and it is not worth doing PCA at all? Is the floor ...
1k views

### Values for Heston Model Parameters

Under the Heston model, the stock price and volatility follow the processes \begin{align*} dS & = \mu S dt + \sqrt{V} S dW^1, \\ dV & = \kappa (\theta - V)dt + \sigma \sqrt{V} dW^2, \\ dW^1 dW^...
84 views

### Benchmarking option pricing under stochastic interest rates

I priced a long-term option (10 or 20 years) using two different models: one assumes constant interest rates, the other assumes stochastic interest rates. Is there a way (e.g. a benchmark) to ...
58 views

### Compare performance buy-and-hold strategies after stock-split

QUESTION: How should I analyze the statistical significance of the difference between two buy-and-hold strategies (or the relative performance) when the samples are not independent? Background: I ...
29 views

### Do I need to update the standard deviation into GARCH for the next step conditional variance predict?

I need to compare two garch models, I try to do that by Value at Risk. In general, if I have an initial conditional variance, for example, h1, then I can predict the next N days conditional variance ...
1k views

### bond price formula in excel

I inherited a excel spreadsheet that has the following code to price a bond given coupon and current yield ...
69 views

### Which bond corresponds to which curve?

Bond X has a coupon Bond Y is a zero-coupon bond (Maturity 2 years) Bond Z is a zero-coupon bond (Maturity 10 years) The following graph is given: X-axis: yield curve, Y-axis: price Question: Which ...
246 views

### Seeking Advice for Exam FM regarding Derivatives Markets

I am taking Exam FM in a week and I was wondering if I could get any advice from people who have recently passed this exam. How much of the derivatives markets question did show up? I am using the ...
498 views

### How to optimally hedge construction loans with interest rate swaps?

We are a borrower with a construction loan that is pay floating. At the inception of the loan, we entered into a pay-fixed/receive-floating interest rate swap with a growing notional profile that ...
96 views

### How do I find the Sharpe Ratio?

Suppose I'm given two assets, $x_0$, $x_1$ and the stochastic discount factor m. How do I find $m_p$, then use it to compute Sharpe($R_p$)? Any help is greatly appreciated.
126 views

### Active or Passive strategy?

From my reading, passive portfoliomanagement means to replicate an index, active portfoliomanagement means to deviate from an index. Does that mean that e.g. rules-based investing is actually an ...
63 views

### How to implement an Interest rate neutral strategy using options?

Intuitively one would think that investing equal amounts in an ETF such as TLT and an short ETF such as TBF (with some factor for the interest rate payout of the long fund) should result in a interest ...
63 views

### VIX For Convertible Bonds

Is there something similar to the VIX but related to the convertibles bonds market in the U.S. ? Thanks, Max.
746 views

### Black-Litterman with simple portfolio

In an attempt to learn Black-Litterman I have come across this "simple" example. Suppose that you analyze market data using CAPM $$r_i-r_f=\beta_i(r_m-r_f)+\epsilon_i$$ Suppose there are 2 assets in ...
39 views

### dynamic programming with serially independent returns

Book suggests that "asset returns are assumed to be serially independent, so wealth is a single state connecting one period to the next". I understand path dependency is lost in case of serial ...
608 views

### Is the Volatility of the Fx Inverse process same as Fx

Let St = Fx and St(Inverse) = 1/Fx. Do both of these have same volatility and if so how would you prove it?
92 views

### How to prove following order?

Consider a consol bond, i.e. a bond which will forever pay one unit of cash at $t = 1, 2, . . ..$ Suppose that the market yield $y$ is constant for all maturities. (a) Compute the price, at $t = 0$, ...
527 views

### How to reduce fx currency pairs ? PCA or other tools?

I have 19 currency pairs like USD.AUD, USD.CAD, etc. Also 82 cross currency pairs like AUD.CAD, EUR.AUD,EUR.CAD etc. When I look to their graphs, most look similar, so I want to reduce number of pair ...
169 views

### negative probabilities in the bivariate tree heston model

I am trying to implement the bivariate tree approach for the Heston model by Beliaeva and Nawalkha. I currently have the problem that given the specifications in their examples, I always obtain ...
646 views

### Calibration Problem in the LMM-Skew (Shifted Diffusion) Model

I have implemented the LIBOR market model (LMM) and I am quite satisfied with the results. I have now added a skew to the model as described in 10.1 of Brigo/Mercurio. That is, I have replaced the SDE ...
220 views

### CVA formula proof

I'm struggling to prove the CVA formula in this paper. Equation (3) is the result of computing the expectation of formula (1). Could you please show me how to prove that?
562 views

### Which size of constant range bar gives the most persistent chart?

A constant range bar chart is like a candle chart, only the candles don't close after a certain amount of time (i.e. 30 min, 4 hours), but after a certain range (i.e. 5 ticks) has been crossed. So if ...
651 views

### Convexity of Portfolio Containing Eurodollar Future and Forward Rate Agreement

Assume an individual is a buyer, i.e., long, of one Forward Rate Agreement and a seller, i.e., short, of one Eurodollar Futures contract. Does the collective portfolio have positive or negative ...
137 views

### Stochastic Volatility for Stocks, FTSE

Can someone help me with calculating Stochastic Volatility (of stocks and options) using SAS or R or Matlab please? I am new to SAS and I am trying to use Heston model, White-Hull model or any other ...
61 views

### Engle Granger test returns a 0 in matlab, while correlation factor is .80+. Am I doing something wrong?

Engle Granger test is giving me a ans = 0. The correlation factor is: 0.8+ Does this imply the No cointegration hypothesis is true? i.e. as per my understanding that there is cointegration? I am ...
53 views

### Significance of Data

The following is a result I get from a pair trading model. I am trying to figure out the significance of the below but failing. Can someone help me out i.e. a resource or possibly an explanation on ...
39 views

### measuring the performance of round-trips on stocks

can you provide me with some ideas to assess the profitability of round-trips? That is when I buy 100 shares of IBM at 10\$and I resell them two days later at 11\$, how can I measure the profit made? ...
54 views

### Rational expectation meaning

What does rational expectation (RE) mean in agent-based modeling context? What are the relationships between RE and expectation and outcome?
774 views

### R or Matlab code for Multi-Barrier-Options (3 or more underlyings)

I am looking for R or Matlab code examples of multi-barrier-options (or multi-barrier reverse convertibles) with at least 3 underlyings. Do you have such code or can you point me to a place where I ...
141 views

### Rate of Return Required on Buying Stocks with Loan

A bank gives a loan $L$ for $m$ months and the monthly interest rate is $i$. The bank requires monthly installments - which I calculate is $I = \frac{L}{m} + Li$. I use this loan to buy stocks....
84 views

### Input for unanticipated risk premium estimation

In the paper "Economic Forces and the Stock Market" by Chen, Roll and Ross, unanticipated risk premium (URP) is tested as a potential risk factor for stock returns. This factor is commonly calculated ...
139 views

### Black (1976) model: boundary conditions with non-convergence of spot and forward prices

Let's suppose we have a futures contract F in a market where the relation $$F(t,T)=S(t)e^{r(T−t)}$$ doesn't hold. What are the the boundary conditions for the derivation of the Black (1976) formula?...
116 views

### DCF of Arbitrary Dates Cash Flows

I am having a problem understanding discounted cash flows. I appreciate your patience and help. Lets say I have a bond that I want to price. ...
650 views

### what is a reasonable beta in CAPM?

I want to predict expected returns for assets using a CAPM, to calculate unexpected (unpredictable, idiosyncratic, non-systemic) returns in portfolios. My CAPM estimated on monthly total gross ...
76 views

### Real value of small numbers of shares of company stock

What is the real value of a single share of company stock? Let's ignore the "the value is what someone is willing to pay for it" angle. At some point, there has to be a real inherent value to ...
173 views

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### Does QuickFIX set PreviouslyReported field itself?

I'm using QuickFIX C++ engine in my project. I send a TradeCaptureReport message to a counter party. There's a field named PreviouslyReported in this message. I set this value to N in the message ...
142 views

### (Self studying) Finding data on Bloomberg

I apologize for asking this very simple question, but I was reading through this chart for the first time, and I would like to know where on Bloomberg can I find data like these, since I have to price ...
306 views

### Default Probability calculation. How to solve system of 2 non linear equations?

I am trying to repeat calculations from Hull(options futures and other derivatives) chapter "Using Equity Prices to Estimate Default Probabilities". I want to solve system of 2 equations: \begin{...
171 views

### Implied volatility in parametric VaR

I'm calculating 1-day parametric VaR estimates for a stock index under the simple assumption that the returns are normally distributed. My question is, what is your opinion of using a volatility index ...