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by EdisonCruise
May 17th, 2014, 12:31 pm
Forum: General Forum
Topic: How to price a collar more accurately?
Replies: 6
Views: 4919

How to price a collar more accurately?

<t>Now the spot is S0, one wants to sell a call option strike at 0.8S0 and buy a put option at 1.2S0. With historical volatility and small interest, the Black-Scholes price difference between the call and put option is very small.(1) There is no option traded in the market, so it is difficult to obt...
by EdisonCruise
May 11th, 2014, 1:35 pm
Forum: Technical Forum
Topic: Heston VS SABR model
Replies: 2
Views: 6881

Heston VS SABR model

<t>I got a bit confused about the difference and application of these two implied volatility model.(1) What are the selection criteria of these two models? Under what kinds of situation, which one is better?(2) Heston model is directly designed for spot price, while SABR model is designed for future...
by EdisonCruise
November 30th, 2013, 10:16 pm
Forum: Student Forum
Topic: Change of numeraire in pricing bond option
Replies: 0
Views: 5664

Change of numeraire in pricing bond option

<t>Change of numeraire in pricing bond optionSuppose the interest rate model:dr_t=κ(θ-r_t )dt+σdW ̂_tBond price with maturity at u, where u>T:P_t (u)=exp[A_t (u)-B_t (u) r_t ]where r_t is the only source of uncertainty of bond price.We need to price call option with maturity T:Q_(t=T) (T)=(P_T (u)-K...
by EdisonCruise
October 17th, 2013, 7:32 pm
Forum: Student Forum
Topic: How to interpret the probability in the figure?
Replies: 12
Views: 6512

How to interpret the probability in the figure?

<t>Thank you for your responses. I still hope to understand this type of problem further. Now suppose Y=min(X1, X2). One can get P{Y>=y}=(1-y)^2. From the attached figure, it can be shown that P{Y>=y and Z<=z} = (z-y)^2. However, can we calculate P{Y>=y and Z<=z} mathematically without the help of f...
by EdisonCruise
October 16th, 2013, 1:27 am
Forum: Student Forum
Topic: How to interpret the probability in the figure?
Replies: 12
Views: 6512

How to interpret the probability in the figure?

<t>Let X1 and X2 be IID random variables with uniform distribution between 0 and 1. z = max(X1, X2).I can calculate the cdf of P{Z<=z}=z^2 analytically. But how to interpret this formula from the attached figure? why the square (0,0)_(z,0)_(z,z)_(0,z) is P{Z<=z}?Thank you. Thank you for your suggest...
by EdisonCruise
October 11th, 2013, 1:47 am
Forum: Student Forum
Topic: How to interpret the expectation and variance in this case?
Replies: 1
Views: 5801

How to interpret the expectation and variance in this case?

The default probability p of bond A is 0.5. Let X be the indicator for the event that bond A defaults. Then the expectation of X is 0.5, and variance of X is p(1-p)=0.25.I cannot understand what the meaning of expectation of X is. Also how can we calculate the variance of X in that way?
by EdisonCruise
September 24th, 2013, 2:45 am
Forum: Brainteaser Forum
Topic: Can we solve the problem by maringale?
Replies: 5
Views: 7340

Can we solve the problem by maringale?

<t>A gambler starts with an initial fortune of i dollars. On each successive game, the gambler wins $1 with probability p, 0<p<1, or loss $1 with probability q=1-p. He will stop if he either accumulates N dollars or loses all his money. What is the probability that he will end up with N dollars?Assu...
by EdisonCruise
September 15th, 2013, 1:36 am
Forum: Brainteaser Forum
Topic: The Dart game problem
Replies: 3
Views: 8328

The Dart game problem

<t>Jason throws two darts at a dartboard, aiming for the center. The second dart lands farther from the center than the first. If Jason throws a third dart aiming for the center, what is the probability that the third throw is farther from the center than the first? Assume Jason's skillfulness is co...
by EdisonCruise
September 7th, 2013, 1:11 am
Forum: Brainteaser Forum
Topic: What's the expected return of this game?
Replies: 3
Views: 7805

What's the expected return of this game?

<t>Thank you Vanubis1. I think it makes sense.I also wonder if there is any quick way to solve E(n)=(3+4+5+6)/6-n*4/6+2/6*E(n+1)?What I can think is let E(n)=an+b. Then we have2a*n+2b=a+9-2nLet n= 1,2we can solve a = -1 and b =4.Finally check if E(n)=4-n a solution. In this way, I am not sure if the...
by EdisonCruise
September 6th, 2013, 1:22 am
Forum: Brainteaser Forum
Topic: What's the expected return of this game?
Replies: 3
Views: 7805

What's the expected return of this game?

<t>There is a dice with number from 1 to 6. You pay 1 dollar to roll the dice each time and you get the return as the dice number. What's your expected return?I try to solve it in this way. I list the return (gained-paid) in each round against the dice number below: dice number 1 2 3 4 5 6return rou...
by EdisonCruise
August 1st, 2013, 4:14 am
Forum: Brainteaser Forum
Topic: tie ropes to form a ring
Replies: 10
Views: 9800

tie ropes to form a ring

there are 100 ropes ? if you tie 100 ends together, what would be the expected number of ropes that would have tied to their own end and be in a ring?
by EdisonCruise
August 1st, 2013, 4:10 am
Forum: Student Forum
Topic: How to calculate conditional expectation?
Replies: 0
Views: 6601

How to calculate conditional expectation?

Assume X and Y are independent variable, f(x) and g(y) are their probability density functions. Can the conditional expectation E{X=x|X+Y<3} be calculated as below?
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