The tag has no usage guidance.

learn more… | top users | synonyms

2
votes
0answers
190 views

Measure change in a bond option problem

This is not a homework or assignment exercise. I'm trying to evaluate $\displaystyle \ \ I := E_\beta \big[\frac{1}{\beta(T_0)} K \mathbf{1}_{\{B(T_0,T_1) > K\}}\big]$, where $\beta$ is the ...
2
votes
0answers
155 views

Optimal stop-loss reinsurance

What are some methods for optimizing stop-loss reinsurance? I've found an article on the minimization of the variance. I also know about the method of average-at-range. Can we apply a method for ...
1
vote
1answer
83 views

Get discount factors with limited knowledge?

I am facing the problem of just having this information: 6% coupon bond with 2.5 years to maturity, traded at a 100% clean price 4% coupon bond with 1.5 years to maturity, traded at a 98% clean price ...
1
vote
2answers
43 views

Perpetual American options

Formulate and solve the free boundary problem for the perpetual American options with the following payoffs. a.) $(S - K)_{+} + a$ where $a > 0$ b.) $(K - S)_{+} + a$ where $a > 0$ ...
1
vote
1answer
48 views

Implied Expected Stock Return from European Option Prices

We can calculate the expected stock return (under the measure $Q$) from at-the-money ($K=S_t$) option prices as: $$E\left(\frac{S_T-S_t}{S_t}\right)=\frac{e^{rT}}{S_t}(C_t-P_t)$$ The result is ...
1
vote
1answer
73 views

Preparation for interview: influx of power of the moon

I am preparing myself for an interview for a quantitative analyst position and one of the sample questions asked in previous examinations was: "Suppose the moon were to disintegrate, and fall to ...
1
vote
1answer
57 views

Is it possible that some types of financial systems can resonate?

Financial systems can certainly be modeled using the same tools physicists use to model dynamic physical systems. The validity of such is evidenced by models such as that developed by Black and ...
1
vote
1answer
175 views

derivation of heston pde in gatheral

Following Gather (the volatility surface, chapter 2) we assume the following process: $$ dS_t = S_t(\mu_t dt+\sqrt{\nu_t}dZ^1_t)$$ $$ d\nu_t= -\lambda(\nu_t-\bar{\nu})dt+\eta\sqrt{\nu_t}dZ^2_t$$ ...
1
vote
1answer
177 views

Arrow-Debreu Price in “The Volatility Smile and its implied Tree”

I was reading the old, but still interesting paper "The volatility smile and its implied tree" by Derman and Kani. I have a two questions about the derivation of the $2n+1$ equations, both of them ...
1
vote
2answers
95 views

Weighting with restrictions, but no clear objective function?

I have 40 shares in an index and I want to weight them based on their market value, define the known value as $x_i$ In the traditional way, the weight of each share is calculated as: $w_i = x_i / \...
1
vote
1answer
60 views

Why is the discount function non increasing if pure cash holdings are feasible?

I am struggeling with the question, for example lets take a swap with rate of 3.2 for one year and 3.6 for 2 years and Discount Factor 0.96899 for the first year and 0.93158 for the second year. ...
1
vote
2answers
66 views

Black-Scholes and Markovian contingent claim

Background information: Proposition 4.1 - For a European Markovian contingent claim, the Black-Scholes price satisfies $$\Theta(\tau,S) = -\frac{\sigma^2 S^2}{2}\Gamma(\tau,S) - rS\Delta(\tau,S) + rV(...
1
vote
1answer
95 views

Stochastic calculus: what am I doing wrong?

it is just the computation of a second moment but however is creating debate !!... Can someone spot the error?
1
vote
1answer
54 views

How to rightfully balance the share of the organization between departments after variable changes?

This is an abstracted version of the problem I'm facing and I have to tell you first, my question might not be precise and or even correct, so I hope you understand and in that case can improve the ...
1
vote
1answer
48 views

Symmetric probability and subjective return

Let $\{Z_k\}_{k=1}^{N}$ be a sequence of i.i.d. random variables with the following distribution $$Z_k = \begin{cases} \alpha &\text{with probability} \ \hat{\pi}\\ -\beta &\text{with ...
1
vote
1answer
106 views

Pricing of Black-Scholes with dividend

Consider the payoff $g(S_T)$ shown in the figure below. Consider Black-Scholes model for the price of a risky asset with $T = 1$, $r = .04$, and $\sigma = .02$ and dividends are paid quarterly with ...
1
vote
1answer
54 views

Desperate for help with simple derivative

Can someone help explain how differentiating the following with respect to $x$: $$ \frac{1}{2} \alpha \mathbf{x}^T \Sigma \mathbf{x} + (\mathbf{\mu} - R\mathbf{1})\mathbf{x} $$ Yields the following: ...
1
vote
0answers
50 views

Replicating American call option

Consider a two-period binomial model for a risky asset with each period equal to a year and take $S_0 = 1$,$u = 1.2$, and $l=0.8$. The interest rate for both periods is $R = .05$ a.) If the asset ...
1
vote
0answers
70 views

Two-period binomial model for American option

Consider a two-period binomial model for a risk asset with each period equal to a year and take $S_0 = 1$, $u = 1.5$, and $l = 0.6$. The interest rate for both periods is $R = .1$. a.) Price an ...
1
vote
1answer
68 views

Find the solutions of the ODE from SDE

Consider the SDE $$dS_t = rS_t dt + \sigma S_t dB_t \ \ \ \text{where} \ r \ \text{and} \ \sigma \ \text{are constants}$$ a.) Find the ODE for the function $V(x)$ such that $e^{-rt}V(S_t)$ is ...
1
vote
0answers
35 views

Find the PDE for a function that makes it a martingale

Given the SDE, find the PDE for the function $V(t,x)$ such that $V(t,S_t)$ is a martingale. $dS_t = \kappa(m - S_t)dt + \sigma\sqrt{S_t}dB_t$ where $\kappa$,$m$, and $\sigma$ are constants. ...
1
vote
0answers
78 views

Understanding Price Elasticities in Discrete Choice Models (Derivative)

I'am in the midst of a paper on mutual fund product differentiation by Li and Qiu. Here, the authors model the utility an investor derives from investing in a mutual fund using a Discrete Choice Model ...
1
vote
0answers
75 views

Sampling and/or asymptotic distribution of a function

Assume we have the following function: $$f(p) = \frac{1}{(1-p)d}\ln\left(\frac{1}{T}\sum_{t=1}^{T}\left[\frac{1+X_t}{1+Y_t} \right]^{1-p} \right)$$ where $d$ is a constant $T$ is a constant $X_t$ ...
1
vote
0answers
123 views

What is the right group of durations?

It seems that the group of durations commonly used in quantitative analyse is $\mathbf{R}$ but it seems to me that $\mathbf{R_+^*}$ could also be an interesting choice. While I am not aware of ...
1
vote
0answers
113 views

Does it make sense to apply complicated mathematics to calculate with precision when the margin of error is +/-10%? [closed]

This is more of a philosophical question than general question. Quantitative finance applies highly complicated mathematics and has attracted very smart people to this field lately given the high pay ...
1
vote
0answers
97 views

How to show that the risk contribution function is or is not injective?

Assume a portoflio $w \in \mathbb{R}^n$, you can get the total risk contribution $\psi_i$ of asset $i$ by doing: $$\psi_i = w_i \frac{\partial \sigma(w)}{\partial w_i}= \frac{1}{\sigma(w)} \left[ w_i^...
0
votes
3answers
107 views

Put-Call Parity Application

In the binomial model, how that the Delta of a call option $\Delta^{call}$ and the Delta of a put option $\Delta^{put}$ with the same maturity and strike satisfy $$\Delta^{call}_t - \Delta^{put}_t = ...
0
votes
1answer
44 views

Payoff of option

Consider the payoff $g(S_T)$ shown the figure: I believe the payoff represented as a linear combination of the payoffs of some options with different strike and same maturity $T$ is $$g(S_T) = (...
0
votes
1answer
29 views

Binomial Model, Number of nodes from $t = 0$ to $t = n$

How many paths are there in a binomial model from time $t = 0$ to time $t = n$? How many nodes (states) are there? Intutively it seems that there are $2^n$ paths and $2n - 1$ nodes. But I am not sure ...
0
votes
1answer
907 views

Determine state price vectors?

I have 3 states with two assets, stocks and bonds. The bond has a payoff of 1 in every state of the world. And the stock has a current price of $S_0 = 100$ and ...
0
votes
1answer
45 views

Replicating option strategies

I was curious if there was any references to replicating option strategies i.e. bull spread, bear spread, butterfly, strangle, straddle, etc...? Also what is the insight into replicating of these ...
0
votes
3answers
78 views

Linear combination of payoffs of bull and bear spreads

Write the following payoffs as linear combination of call options with different strikes and possibly some cash and give the closed form formula for them. Attempted solution: The payoff for the bear ...
0
votes
1answer
32 views

two-period binomial model, with price that is path-dependent

Consider a two-period binomial model for a risky asset with each period equal to a year and take $S_0 = 1$, $u = 1.03$ and $l = 0.98$. How do you price a look-back option with payoff($\max_{t=0,1,2}...
0
votes
1answer
51 views

Convexity in Markovian contingent claim

Background information: I believe we can use Jensen's Inequality here Show that if the payoff function $V(S_T)$ is a convex function on $S_T$, then the Markovian European contingent claim with ...
0
votes
1answer
54 views

European Markovian option

Background information: Consider a European contingent claim with payoff $V(S_T)$, where $V: \mathbb{R}_+\rightarrow \mathbb{R}$ is a function which assigns a value to the payoff based on the price of ...
0
votes
1answer
81 views

Arrow-Debreu Model and Risk-Neutral Probabilities

Consider one period Arrow-Debreu model with $N = 2$ and $M = 4$ shown in Figure 3.5 and take $R = 0$. a.) Show that any risk neutral probability $\hat{\pi} = (\hat{\pi}_1, \hat{\pi}_2, \hat{\pi}_3, \...
0
votes
1answer
28 views

How to calculate 5 years return & STD for ETF?

I want to calculate by-myself 5 year return & STD for SPY ETF. What I did: Downloaded to Excel from yahoo finance historical data for the ETF (daily Adj. Close) from ...
0
votes
1answer
137 views

How can we write swap as a chain of FRA's

For the rest of my question I use the notation from Brigo. The discounted payoff of a receiver interest rate swap (RFS) at $t<T_{\alpha}$, where $T_{\alpha}$ is the first resetting date, is given ...
0
votes
2answers
66 views

Two-period binomial model with dividends

Consider a two-period binomial model for a risky asset with each period equal to a year and take $S_0 = 1$, $u = 1.15$ and $l = 0.95$. The interest rate is $R = .05$. a.) If the asset pays 10% of its ...
0
votes
0answers
36 views

Return, STD and CAPM based on Continuously compound return on daily prices

Mission: For some ETF, Get 1, 3, 5 years: Return STD CAPM parameters (alpha, beta) Reference if I calculated correctly: Yahoo finance performance & risk data Raw data: Daily adj. close ...
0
votes
0answers
19 views

Question in the proof of “Optimization of conditional value-at-risk”

I'm reading the paper "Optimization of conditional value-at-risk" by Rockafellar and Uryasev. The state two theorems within the paper which are proven in the appendix. Let me introduce some notation ...
-1
votes
2answers
215 views

What's the first time-integral of price called?

In general I'm wondering about the names of time-derivatives of price. E.g. in physics the first few time-derivatives of position are: f(x) = displacement f'(x) = velocity f''(x) = acceleration ...
-1
votes
1answer
97 views

Math basics of Equally-weighted Risk contributions

i'm writing my BA Thesis about "Equally-weighted Risk contributions". Can anyone recommend math books for further understanding of Risk contributions?