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3
votes
0answers
129 views

Log-normal mixture models for implied volatility

My question is about a the proof that can be found in the following article by Brigo et al. https://people.kth.se/~lang/arkiv/finans/exjobb/anton/lognsmil.pdf The main definitions and formulas need ...
2
votes
2answers
87 views

Sums of random variables and independence

I'm having troubles with this proof: Let $\{Z_i\}_{i\in\mathbb{Z}}$ be i.i.d. random variables with zero mean and unit standard deviation. For $(a_0, a_1, ..., a_r)$ a sequence of $r$ real numbers ...
3
votes
1answer
93 views

How to prove the “Law of one price” theorem?

There are two subparts to Fundamental Asset Pricing theorem. The Law Of One Price (LOOP thereafter) holds if and only if there exists a state price vector. In a market in which the LOOP holds, the ...
5
votes
1answer
132 views

Proving that Absence of Arbitrage does not imply law of one price

I am trying to prove that the Absence of arbitrage statement (AOA) does not necessarily imply the law of one price (LOP). For the definitions of these concepts I am using Cochrane's book "Asset ...
1
vote
0answers
75 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?
1
vote
1answer
237 views

Trading over a Ornstein/AR process

For a OU/AR(1) process is there anyway to analytically calculated most probable period of time the process is likely to diverge from the average, before turning to converge. Basically I am looking ...
5
votes
1answer
186 views

Heat/Diffusion Equation

I am working on a problem where I have successfully reduced a version of Black Scholes to the Heat Equation and then shown the solution to be: ...
9
votes
2answers
549 views

Is it possible to understand financial theory without mathematics?

I am trying to develop a short course on financial theory, covering the fundamentals of forward and options pricing, and 'efficient market' theory. I want to reduce the amount of mathematics to a ...