qu.1.topic=Single Period Binomial Model@ qu.1.1.mode=Multiple Selection@ qu.1.1.name=Elements of the Single Period Binomial Model@ qu.1.1.question=

The 5 quantifiable elements of the single period binomial financial model are:

@ qu.1.1.choice.1=

A single interval of time, from $t=0$, to $t=T$.

@ qu.1.1.choice.2=

A single stock of initial value $S$,

@ qu.1.1.choice.3=

In the time interval the stock can increase by a factor $U$ to value $SU$ with probability $p$, and it can decrease in value by factor $D$ to value $SD$ with probability $q=1-p$.

@ qu.1.1.choice.4=

A single bond with a continuously compounded interest rate $r$ over the interval $T$.

@ qu.1.1.choice.5=

A market for derivatives (like options) dependent on the value of the stock at the end of the period.

@ qu.1.1.choice.6=

Changes in prices may be random, but are continuous with some probability distribution

@ qu.1.1.choice.7=

@ qu.1.1.choice.8=

Only integer amounts of the stock and bond can be purchased

@ qu.1.1.choice.9=

Dollar amounts are very large

@ qu.1.1.choice.10=

Only a few traders are involved

@ qu.1.1.choice.11=

@ qu.1.1.choice.12=

The law of supply and demand holds

@ qu.1.1.info=@ qu.1.1.answer=1 2 3 4 5 @ qu.1.2.mode=Blanks@ qu.1.2.name=A portfolio of the stock and the bond@ qu.1.2.question=

A portfolio of the stock and the bond which will have the same value as the derivative itself in any circumstance is called a <1>.

@ qu.1.2.grader.1=text@ qu.1.2.blank.1=replicating portfolio@ qu.1.2.info=@ qu.1.3.mode=True False@ qu.1.3.name=Realistic Assumption on parameters@ qu.1.3.question=

True or False: For the single period binomial model, a realistic financial assumption about the factors of change $U$ and $D$ would be that $D.

@ qu.1.3.choice.1=

True

@ qu.1.3.choice.2=

False

@ qu.1.3.info=@ qu.1.3.answer=1 @ qu.1.4.mode=Blanks@ qu.1.4.name=Any amount of stock or bond@ qu.1.4.question=

We make the assumption that the stock and bond are <1>, that is we can buy them in any amounts.

@ qu.1.4.grader.1=text@ qu.1.4.blank.1=divisible@ qu.1.4.info=@ qu.1.5.mode=Blanks@ qu.1.5.name=Negative position in stocks@ qu.1.5.question=

We make the assumption that the stock and bond are divisible, we can buy them in any amounts including negative amounts which are called <1> positions.

@ qu.1.5.grader.1=text@ qu.1.5.blank.1=short@ qu.1.5.info=@ qu.1.6.mode=Blanks@ qu.1.6.name=Setting up the portfolio@ qu.1.6.question=

There are two <1> for the amounts of stock and bond to buy for the portfolio, and we have two expressions to match with the two values of the derivative!

@ qu.1.6.grader.1=text@ qu.1.6.blank.1=unknown quantities@ qu.1.6.info=@ qu.1.7.mode=Blanks@ qu.1.7.name=Two expressions@ qu.1.7.question=

In the single period binomial model we have two expressions to match with the two values of the <1>.

@ qu.1.7.grader.1=text@ qu.1.7.blank.1=derivative@ qu.1.7.info=@ qu.1.8.mode=Numeric@ qu.1.8.name=Evaluating call option increase@ qu.1.8.question=

Consider a call option on a stock with current price $\left\{p\right\}$. At expiration, the stock price could be either a factor $U=\left\{u\right\}$ higher or a factor $D=\left\{d\right\}$ lower. The strike price is $K=100$. If the stock price goes higher, then the payoff $f\left(SU\right)$ will be:

@ qu.1.8.answer.num=\${ans}@ qu.1.8.answer.units=@ qu.1.8.showUnits=false@ qu.1.8.algorithm= \$p = range(95,105); \$u = range(107,115)/100; \$d = range(85,95)/100; \$ans = \$p*\$u - 100; @ qu.1.8.info=@ qu.1.8.grading=exact_value@ qu.1.9.mode=Numeric@ qu.1.9.name=Evaluating call option decrease@ qu.1.9.question=

Consider a call option on a stock with current price $\left\{p\right\}$. At expiration, the stock price could be either a factor $U=\left\{u\right\}$ higher or a factor $D=\left\{d\right\}$ lower. The strike price is $K=100$. If the stock price goes lower, then the payoff $f\left(SD\right)$ will be:

@ qu.1.9.answer.num=\${ans}@ qu.1.9.answer.units=@ qu.1.9.showUnits=false@ qu.1.9.algorithm= \$p = range(95,105); \$u = range(105,115)/100; \$d = range(85,95)/100; \$ans = 0; @ qu.1.9.info=@ qu.1.9.grading=exact_value@ qu.1.10.mode=Numeric@ qu.1.10.name=Evaluating put option@ qu.1.10.question=

Consider a put option on a stock with current price $\left\{p\right\}$. At expiration, the stock price could be either a factor $U=\left\{u\right\}$ higher or a factor $D=\left\{d\right\}$ lower. The strike price is $K=100$. If the stock price goes higher, then the payoff $f\left(SU\right)$ will be:

@ qu.1.10.answer.num=\${ans}@ qu.1.10.answer.units=@ qu.1.10.showUnits=false@ qu.1.10.algorithm= \$p = range(95,105); \$u = range(107,115)/100; \$d = range(85,95)/100; \$ans = 0; @ qu.1.10.info=@ qu.1.10.grading=exact_value@ qu.1.11.mode=Numeric@ qu.1.11.name=Evaluating put option@ qu.1.11.question=

Consider a put option on a stock with current price $\left\{p\right\}$. At expiration, the stock price could be either a factor $U=\left\{u\right\}$ higher or a factor $D=\left\{d\right\}$ lower. The strike price is $K=100$. If the stock price goes lower, then the payoff $f\left(SD\right)$ will be:

@ qu.1.11.answer.num=\${ans}@ qu.1.11.answer.units=@ qu.1.11.showUnits=false@ qu.1.11.algorithm= \$p = range(95,105); \$u = range(105,115)/100; \$d = range(85,95)/100; \$ans = 100 - \$p*\$d; @ qu.1.11.info=@ qu.1.11.grading=exact_value@