| Portfolio insurance (PI) is a dynamic investment technique which aims to protect the underlying portfolio while simultaneously retaining some upside potential. Option-based portfolio insurance (OBPI), constant proportion portfolio insurance (CPPI) and time-invariant portfolio protection (TIPP) are the most popular PI strategies in the mar-ket of capital guaranteed products. Some previous studies show that CPPI-and TIPP-managed portfolios are exposed to gap risk when asset prices exhibit discontinuous moves (jumps) or continuous trading is infeasible because of illiquidity or transaction costs. In the presence of gap risk, the issuers or the managements of the rate of return guaranteed products have to turn to third parties for guarantee or reinsurance. How to figure out a proper reinsurance rate or a proper reinsurance fee is an important practi-cal issue. The existing literature focus on the valuation of CPPI-managed rate of return guaranteed products and fail to incorporate the synthetical effects of market frictions such as jumps in asset prices, position constraints, stochastic interest rate and discrete-time trading. Moreover, there is no paper exploring the valuation of the TIPP-managed rate of return guaranteed products. Performance evaluation and comparison is anoth-er important topic on PI strategies. Existing literature on the topic merely take into consideration the effects of proportional transaction costs and some per-specified re-balancing rules (e.g. daily rebalancing) and fail to incorporate the effect of price impact and rebalancing disciplines.The thesis investigates PI strategies in a market of frictions from the following two aspects:first, it comprehensively incorporates the synthetical effects of jumps, position constraints, stochastic interest rate and discrete-time trading and systemati-cally explores the pricing issue of CPPI-and TIPP-managed rate of return guarantees; second, it introduces the effect of price impact and employs Monte Carlo simulations and historical simulations to conduct the performance evaluation and comparison of PI strategies. The main conclusions of the thesis are listed as follows:First, the thesis obtains analytic pricing results of CM-managed single period ab-solute return guarantee and multi-period relative return guarantee and extends the coun-terpart pricing results in Wang and Liu [1] by incorporating the effect of jumps in asset price.Second, in the specification of single period absolute return guarantee,(1) there is no gap risk with both CPPI and TIPP strategies and the prices of the return guar-antees are zero under continuous trading.(2) in the presence of jumps in asset price, gap risk arises with both CPPI and TIPP and the prices of return guarantees under the management of both strategies are positively correlated with the multiple and the guarantee level, irrespective of position constraints. Furthermore, the introduction of position constraints significantly decreases the prices of the return guarantees for both strategies and exhibits stronger effect with bigger multiple.(3) the volatility parameter of the risky asset has no effect on the prices of the return guarantees for both strategies under continuous trading, irrespective of jumps in asset price.(4) the price of TIPP-managed return guarantee is negatively correlated with the floor percentage parameter.(5) the prices of the return guarantees for both strategies are positively correlated with rebalancing period.Third, in the specification of multi-period relative return guarantee,(1) the prices of the return guarantees for both strategies are positively correlated with the multiple and the volatility parameter of the risky asset, regardless of the continuity of price path of the risky asset, position constraints and the rebalancing style.(2) the price of CPPI-managed return guarantee is positively correlated with the guarantee level in the presence of jumps in asset price, regardless of position constraints, while the relation between the price of CPPI-managed return guarantee and the guarantee level depends on the presence or absence of position constraints when the risky asset exhibits jump-s.(3) the price of TIPP-managed return guarantee is positively correlated with the guarantee level and negatively correlated with the floor percentage, irrespective of the continuity of price path of the risky asset, position constraints and the rebalancing style. (4) if the parameter of guarantee level is set the same way in each subperiod, the price of CPPI-managed return guarantee is uncorrelated with the investment horizon while its TIPP counterpart is positively correlated with the investment horizon, irrespective of the continuity of price path of the risky asset and position constraints.(4) the rebalanc-ing period has positive effect on the prices of the return guarantees for both strategies, irrespective of the continuity of price path of the risky asset and position constraints.Fourth, the Monte Carlo simulations suggest that,(1) the optimal rebalancing dis-ciplines for CM are lag discipline in a market of low price impact and market move discipline in a market of high price impact;(2) lag discipline is the optimal rebalanc-ing discipline for both OBPI and TIPP in both market conditions;(3) market move discipline and time discipline are the optimal rebalancing discipline for CPPI strategy in a market of low and high price impact, respectively;(4) there exists no first order stochastic dominance between the three PI strategies (OBPI, CPPI and TIPP) and the two simple strategies (BH and CM);(5) OBPI has three order stochastic dominance over CM in both market conditions but only three order stochastically dominates BH in a market of high price impact;(6) both CPPI and TIPP have second order stochastic dominance over BH, CM and OBPI in both market conditions;(7) there is no stochastic dominance of up to order3between TIPP and CPPI.Fifth, there exists significant nonlinear price impact in the Chinese stock market and the marginal price impact is significantly decreasing. The historical simulations show that, time discipline is the optimal rebalancing discipline for CM while the three PI strategies (OBPI, CPPI and TIPP) share market move discipline as their optimal rebalancing discipline. The three PI strategies (OBPI, CPPI and TIPP) is significantly better than the two simple strategies (BH and CM). CPPI performs better than OBPI while TIPP performs better than both OBPI and CPPI.The contributions of the thesis to the existing literature are three-fold. Firstly, when exploring the pricing issues of CPPI-and TIPP-managed rate of return guaran-tees, it comprehensively takes into consideration market frictions such as jump in asset price, position constraints, stochastic interest rate and discrete-time trading. Secondly, it investigates the issue whether or not there exists an optimal rebalancing discipline for each PI strategy in a market of price impact for the first time. Thirdly, it incorporates the effect of price impact and rebalancing discipline into the performance evaluation and comparison of PI strategies. The research in the thesis bases itself on more realistic assumptions and thus can provide more meaningful reference for decision making in the market of rate of return guaranteed products.
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