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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 ...
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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-...
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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 ...
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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 ...
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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^...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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.
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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 ...
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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 ...
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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.
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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 ...
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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 ...
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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?
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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 $t = 0$, ...
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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 ...
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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 ...
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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 ...
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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?
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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? ...
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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?
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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 ...
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1answer
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....
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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 ...
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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?...
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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. ...
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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 ...
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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 ...
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173 views

Exact value of mean reversion rate knowing terminal value of the process

Let you have the following mean reverting process: $\text{d}x_{t}=a(\theta-x_{t})\text{d}t$, where the diffusion term is absent, that is this process is not stochastic. Let you know the value of $\...
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1k views

Correlation Sensitivity

Suppose I have 2 stocks $S_{1}$ and $S_{2}$: \begin{align} & dS_{1}=rS_{1}dt+\sigma_{1}S_{1}dB_{1}\\ & dS_{2}=rS_{2}dt+\sigma_{2}S_{2}dB_{2}\\ & dB_{1}dB_{2}=\rho dt \end{align} Then I ...
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130 views

forward- and backward adjusting stockprices

Do you guys know if a paper has been published that discusses forward- and backward adjusted stockprices, and the look ahead bias coming from backward adjusted data?
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1answer
50 views

Black Scholes Replication If Underlying Does Not Move?

Let's say you are long a call and want to replicate that call buy being short underlying and long bonds. If the underlying moves up in the next period but not enough to cover theta, the option ...
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1answer
60 views

Negative Cost of Debt

I got the the interest expense from Microsoft, it is in negative: -2.73 billion (source: MSFT Annual Report). Does this mean Microsoft is receiving interest instead of paying it? If my cost of debt ...
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1answer
138 views

When $E[f(\alpha,X)] = f(\alpha, E[X])$

When $E[f(\alpha,X)] = f(\alpha,E[X])$, where $f$ is some convex function of the first and second variables, except when the first variable takes the value $\alpha$ in which case the equality holds, ...
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1answer
33 views

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 ...
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1answer
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 ...
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1answer
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{...
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1answer
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 ...
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1answer
62 views

Is there an open architecture API or excel solution for calculating and adjusting bond pricing?

Is there an open architecture API for calculating and adjusting bond prices? I am looking to adjust bond pricing on OAS or adjusted spreads to various indices and need a tool to process large amounts ...
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1answer
3k views

How can an FRA create arbitrage opportunities?

I'm working through Options, Futures and Other Derivatives (beginner trying to understand investment banking). I've more or less followed the discussion of interest rates, forward rates and forward ...

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