6A: 001 Introduction to Financial Accounting
April 17, 2014
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Exam #2
Form A
The exam consists of five questions with the point allocations detailed below. Answers will
Up the Hill Bakery
1st Quarter Financial Projections
Date
Up the Hill Bakery
January
February
March
Total
Sales
Beverage
Bread
Bakery Items
Lunch Sales
Breakfast Sales
$
$
$
$
$
5,500
8,500
7,200
8,40
constructed. The new securities are then called derivative securities.
Our purpose is to set-up a framework, e.g. an enormously large
information tree structure, that is able to accommodate financial
initial price S 0 = $100 and we are considering a four month security.
Take t = one moth, 0 = 0.1/year, = 0.15/year and 2 = 0.04/year,
construct both a binomial tree and binomial lattice. Computer the
contingent claim with the following payoff: X(cfw_aa, ab, ac, ba, bb, bc, ca,
cb, cc) = cfw_1, 2, 3, 4, 5, 6, 7, 8, 9. (ii) The option, not obligation, to
exchange one share of a2 to one share of a1,
S 0 t+t (Bn) S 0 t (B) = e rt+t(B) the discount factor. Finally, we denote
the transition probability from B to Bj by pj := P(Bj | B) = P(Bj ) P(B) .
That P is risk neutral requires p := (p1, , pn) be
Then cfw_SttT can be unit prices of an asset. Note that St3 is not
measurable on (Pt2 ) since it is not a constant on every block in Pt2 .
That is, after knowing the outcome of first two tosses of the
11.93 e 0.1/12 cash and longing 0.676 share of stock, total 11.93
e 0.1/12 + 0.676 19.23 = 0.98. If stock price rises up to 21.58, then
the portfolio is worth 2.89. The writer responds by 3.4. CERTAI
i=1 S t )/3 (The average of past three month). Then the payoff is X =
maxcfw_0 , S3 ( P3 i=1 S t )/3). Tracking the history, we find values of X
and the corresponding probability as follows: history u
the option is valid. This is typically defined as expiration date. There are
quite a number of options types: 1. European option In this option, the
right of the option can be exercise only on the exp
consisting of assets S1, S2, S3 and their derivatives S4, S5, S6, S7. 2.3.
MULTI-PERIOD FINITE STATE MODELS 51 t0 t1 t2 t3 1 2 3 4 5 6
7 8 9 10 Figure 2.1: A Three period Tree Structure 2.3 MultiPerio
combine nodes, so that we can devise a computationally efficient
methods of solution. Here in this section we are developing theoretical
tools, so for simplicity, we always assume that the tree is ful
t (z) = e 0(tT) cfw_p f(su) + (1 p) f(sd). Thus, the portfolio at time t =
tn1 is completely determined by the claim. Now we consider the
general time period from t = tk to tk+1 = t + t. Similar to th
.1318 .1318 0.1174 .1318 .1174 .1174 0.1046 S 3 (k) 86.66 97.26 97.26
109.17 97.26 109.17 109.17 122.53 S 2 (k) 90.89 102.02 102.02 114.51
S 1 (k) 95.33 107.01 S 0 100.00 Here the second line displays
$1000 cash to be received one year from now) has to be discounted to
its present values. Here we introduce a short-term risk-free asset to
perform this job. Given a state space, an asset is short-term
random variable is a measurable function on a probability space. A
stochastic process is a collection cfw_SttT of random variables on a
probability space (, F, P); here T is a set for time such as T =
contingent claims can be easily calculated. Theorem 2.3 (Finite State
Model Pricing Formula) Suppose a state model admits a riskneutral
probability P. Then the initial price of any contingent claim X
(m i)! e 0(tT) f s e(T t)+ t(2im) , m = T t t . The portfolio
replicating the contingent claim is unique. At any time t t and spot
security price s, it consists of nrf (s, t t) shares of risk-free ass
confidence), that the expected annul return rate is 12%5%. From the
example, we see that there is a statistical limitation on the
measurement of data. The lack of reliability is not due to the faulty
expected change is only about 0.05%. The daily mean is low compared
to the daily fluctuation. (3) Suppose we use one year of monthly data,
i.e. T = 1 and p = 12. Then we have SD(t) = / 12 = 1.25%. We
(Hint: In the subtree B cfw_B1, B2, the value Vt of the American call
option is Vt(B) = max n St(B) 180, er [p(B B1)Vt+t(B1) + p(B
B2)Vt+t(B2)]o . The value of the American put is Vt(B) = max n 180
= 1.1 + 1.2 + 1.3 = 3.6. In [t0, t1], the best perform asset is a2 and the
worst perform asset is a0. Hence we short $3.6 from asset a0 and invest
3.6+3.6 = $7.2 on a2; namely, we put nt1 = (3.6/1.1,
Since p is a strongly positive vector and the sum of all its components is
one, we can regard p as a probability measure on , which we call the
risk-neutral probability. Denote by E the expectation op
securities: each cost one dollar with the following pay-off: (i) $3.00 if
the adventure is a high success, $1.00 if moderate success, and $0.00 if
failure. (ii) $6.00 if high success, $0.00 otherwise.
a arbitrage-free state model, there is no difference among the initial
values of portfolios of all self-financing trading strategies that replicate a
same contingent claim. Consequently, the price of